# combined worth of two items

#### eddy2017

##### Full Member
A toy store has a current inventory of 300 robots and dolls. Robots are sold for 35 dollars and dolls are sold for $24 dollars. What is the maximum amount of dolls in stock if the combined worth of the two items in stock is 9,433?. Given Total amount of robots and dolls combined=300 a robot costs$ 35
a doll costs \$ 24
let r be robots
let d be dolls
let m be the maximum amount of dolls in stock if the combined worth of the two items is 9,433?

Reading the problem is easy for me to recognize that robots represent the biggest amount of money in the total.
Any hints?.
Thanks for your prompt and on-target help.
eddy

#### Jomo

##### Elite Member
24r + 35d = 9433
r+d = 300
Solve for r and d

#### Otis

##### Elite Member
Any hints?
Hi eddy. Start experimenting with numbers. (The goal is to form an equation to solve.)

We don't need a symbol for the number of robots. We can express the number of robots in terms of the number of dolls.

Let symbol d represent the number of dolls.

Then the expression 300-d represents the number of robots.

If there were 299 dolls, would the remaining money equal the value of 1 robot?
If there were 298 dolls, would the remaining money equal the value of 2 robots?
If there were 297 dolls, would the remaining money equal the value of 3 robots?

Write out the the arithmetic, for answering those three questions. Do you see that you're doing the same operations?

Now think: if there were d dolls, would the remaining money equal the value of 300-d robots?

Use the pattern of your calculations to try form an equation. If you get stuck, please show us what you tried. Thanks!

#### Jomo

##### Elite Member
Hi eddy. Start experimenting with numbers. (The goal is to form an equation to solve.)

We don't need a symbol for the number of robots. We can express the number of robots in terms of the number of dolls.

Let symbol d represent the number of dolls.

Then the expression 300-d represents the number of robots.

If there were 299 dolls, would the remaining money equal the value of 1 robot?
If there were 298 dolls, would the remaining money equal the value of 2 robots?
If there were 297 dolls, would the remaining money equal the value of 3 robots?

Write out the the arithmetic, for answering those three questions. Do you see that you're doing the same operations?

Now think: if there were d dolls, would the remaining money equal the value of 300-d robots?

Use the pattern of your calculations to try form an equation. If you get stuck, please show us what you tried. Thanks!

There will be a unique solution to this equation. It is possible that this unique solution may not have integer solution (not the case with this problem) but none the less there will be a unique solution. Now it would be an entirely different story if the problem involved inequalities.

#### Otis

##### Elite Member
… Use the pattern of your calculations to try form an equation…
There will be a unique solution to this equation…
Yes, that's correct. It will be a linear equation. Were you trying to point out something about inequalities, for me?

#### Jomo

##### Elite Member
Yes, that's correct. It will be a linear equation. Were you trying to point out something about inequalities, for me?

You did the problem much differently then I did (although the wording through me off and I started off (almost) like you did) and you liked my reply with a WOW so i was thinking that maybe you did not agree that what I did was correct.

#### eddy2017

##### Full Member
You did the problem much differently then I did (although the wording threw me off and I started off (almost) like you did) and you liked my reply with a WOW so i was thinking that maybe you did not agree that what I did was correct.

#### eddy2017

##### Full Member
I will work on the problem tomorrow. Got to turn in for the night. Thanks to all

#### eddy2017

##### Full Member
24r + 35d = 9433
r+d = 300
Solve for r and d
Good morning. Are you asking me two solve the two equations as a system of equations or as a quadratic equation each?.

#### eddy2017

##### Full Member
Hi eddy. Start experimenting with numbers. (The goal is to form an equation to solve.)

We don't need a symbol for the number of robots. We can express the number of robots in terms of the number of dolls.

Let symbol d represent the number of dolls.

Then the expression 300-d represents the number of robots.

If there were 299 dolls, would the remaining money equal the value of 1 robot?
If there were 298 dolls, would the remaining money equal the value of 2 robots?
If there were 297 dolls, would the remaining money equal the value of 3 robots?

Write out the the arithmetic, for answering those three questions. Do you see that you're doing the same operations?

Now think: if there were d dolls, would the remaining money equal the value of 300-d robots?

Use the pattern of your calculations to try form an equation. If you get stuck, please show us what you tried. Thanks!

Otis, thanks for commenting on my problem and for your help. Allow me, pls, to check out Jomo's way first. He replied first. And then I wanna see yours. I don't understand either of them, by the way, so I am really interested in both.

#### eddy2017

##### Full Member
Hi eddy. Start experimenting with numbers. (The goal is to form an equation to solve.)

We don't need a symbol for the number of robots. We can express the number of robots in terms of the number of dolls.

Let symbol d represent the number of dolls.

Then the expression 300-d represents the number of robots.

If there were 299 dolls, would the remaining money equal the value of 1 robot?
If there were 298 dolls, would the remaining money equal the value of 2 robots?
If there were 297 dolls, would the remaining money equal the value of 3 robots?

Write out the the arithmetic, for answering those three questions. Do you see that you're doing the same operations?

Now think: if there were d dolls, would the remaining money equal the value of 300-d robots?

Use the pattern of your calculations to try form an equation. If you get stuck, please show us what you tried. Thanks!

Hi, I do not understand. I am sorry. If you'd care to explain what you meant, please.

#### Jomo

##### Elite Member
You have two linear equations in two unknowns. Look up on YouTube how to solve such problems.

#### eddy2017

##### Full Member
You have two linear equations in two unknowns. Look up on YouTube how to solve such problems.
Yes, I was about to do my research, but was not really sure what to look for. Thanks. I will work on that and show something later.

#### eddy2017

##### Full Member
24r + 35d = 9433
r+d = 300
Solve for r and d
Here is my work.
 24r +35d = 9533
r + d = 300
I will multiply the first equation by 1 and the second equation by -35 to try and eliminate one of the unknowns.
1( 24r +35d = 9533)
-35( r + d = 300 )
let's distribute now
24r+35d=9433
-35r-35d =-10500
I will combine the two equations now.

24r+35d=9433
-35r-35d =-10500

-11r = -1067 ( I will 11 into both sides)
r=97

Now I have solved for one of the variables. To solve for d, I need to use one of the original equations and plug 97 in for r.
I will use the first equation given by Jomo
24r +35d = 9433
24(97)+35d=9433
2328 +35d =9433 (solve for d)
35d=9433-2328
35d=7501 i'll divide 35 into both sides
d=203
So,
r=97 (robots)
d=203 (dolls)
There are 203 dolls in stock.

Let's check
r+d=300
97+203=300 true statement.

#### Subhotosh Khan

##### Super Moderator
Staff member
Here is my work.
24r +35d = 9533
r + d = 300
I will multiply the first equation by 1 and the second equation by -35 to try and eliminate one of the unknowns.
1( 24r +35d = 9533)
-35( r + d = 300 )
let's distribute now
24r+35d=9433
-35r-35d =-10500
I will combine the two equations now.

24r+35d=9433
-35r-35d =-10500

-11r = -1067 ( I will 11 into both sides)
r=97

Now I have solved for one of the variables. To solve for d, I need to use one of the original equations and plug 97 in for r.
I will use the first equation given by Jomo
24r +35d = 9433
24(97)+35d=9433
2328 +35d =9433 (solve for d)
35d=9433-2328
35d=7501 i'll divide 35 into both sides
d=203
So,
r=97 (robots)
d=203 (dolls)
There are 203 dolls in stock.

Let's check
r+d=300
97+203=300 true statement.
You write:

24r +35d = 9533
r + d = 300

What is 'r' and what is 'd'?

Why is 'r' being multiplied by 24 and Why is 'd being multiplied by 35?

Look at your original post - and think!!

#### eddy2017

##### Full Member
You write:

24r +35d = 9533
r + d = 300

What is 'r' and what is 'd'?

Why is 'r' being multiplied by 24 and Why is 'd being multiplied by 35?

Look at your original post - and think!!
You write:

24r +35d = 9533
r + d = 300

What is 'r' and what is 'd'?

Why is 'r' being multiplied by 24 and Why is 'd being multiplied by 35?

Look at your original post - and think!!
Well, r stands for robots
d stands for dolls
Why is 'r' being multiplied by 24 and Why is 'd being multiplied by 35?
Because we want to see the combined worth of both items.
Robots are sold for 35
Dolls are sold for 24
If there is more to your questions than meets the eye, I am not getting it.
I followed the steps to solve two equations with two unknowns in it, like Jomo advised me to do.
That is what I did. I studied it and then came and tried to solve the two equations that Jomo gave me.
The only idea that comes to mind that the variables are being multiplied by the opposite worth in price is because we are trying to find how many more we have of one item than the other.

Last edited:

#### JeffM

##### Elite Member
Solving equations is mechanics: machines can do it. Setting up equations requires thought: minds must do it.

If r represents the number of robots and 35 is the cost per robot, what is the relevance, indeed what is even the meaning, of 24r?

#### eddy2017

##### Full Member
Solving equations is mechanics: machines can do it. Setting up equations requires thought: minds must do it.

If r represents the number of robots and 35 is the cost per robot, what is the relevance, indeed what is even the meaning, of 24r?
That I did not really understand when i saw the equations. I did not set them up. Jomo set them up for me. I should have analysed, though before getting around to solving them. System of equations with two variables in it I have never worked on before. This is my first time.
I would love to know why they were set up that way.

#### JeffM

##### Elite Member
Because Jomo made a mistake. By the way, I teach using Jomo’s method, which I like. He just made a goof.

We have two unknowns. Name them r and d. We need two equations to find two unknowns.

We know the sum of those two unknowns is 300. So, in math, that is r + d = 300.

We also know the total value, which is 9533. So the value of the robots plus the value of the dolls equals 9533.

What is the value of the robots if one robot is worth 35? What is the value of the dolls if one doll is worth 24? So what is our second equation?

EDIT By the way, I am pretty sure that I went through this approach of counting unknowns and finding an equal number of equations in response to an earlier post of yours.

#### eddy2017

##### Full Member
Because Jomo made a mistake. By the way, I teach using Jomo’s method, which I like. He just made a goof.

We have two unknowns. Name them r and d. We need two equations to find two unknowns.

We know the sum of those two unknowns is 300. So, in math, that is r + d = 300.

We also know the total value, which is 9533. So the value of the robots plus the value of the dolls equals 9533.

What is the value of the robots if one robot is worth 35? What is the value of the dolls if one doll is worth 24? So what is our second equation?

EDIT By the way, I am pretty sure that I went through this approach of counting unknowns and finding an equal number of equations in response to an earlier post of yours.
I see now. This is the the other equation that I need it. The mistake was in matching the number with the right variable.
r(35)+d24=9433