Inequalities word problem

[Amb]

Hi I need help

John is packing a package for 8 people (including himself). He wants each person to have at least 2 slices of cakes and 1 drink. Each cake box containing 2 slices of cakes has a volume of 500 cubic centimeter and 1 drink has a volume of 220 cubic centimeters. If the package can hold a volume of 7 litres, find the possible number of drinks in the package.

I tried to solve:

let x be the number of slice of cake and y be the number of drink.

2x+y=1
so 8 person 8(2x+8y)=8

500(x/2)+220y=7000 or 500x+200y=7000

however the question is asking for inequalities and i could not found the correct equation. Please advise.

Thank you

 

[blamocur]

What is the meaning of [imath]2x+y=1[/imath] ?

Also, check you last line of equations -- you have at lest two typos/mistakes there.

 

[Steven G]

2x+y = 1, 1 what????
What does at least 2 mean to you?

How does 500(x/2)+220y=7000 become 500x+200y=7000?

 

[Dr.Peterson]

Hi I need help

John is packing a package for 8 people (including himself). He wants each person to have at least 2 slices of cakes and 1 drink. Each cake box containing 2 slices of cakes has a volume of 500 cubic centimeter and 1 drink has a volume of 220 cubic centimeters. If the package can hold a volume of 7 litres, find the possible number of drinks in the package.

I tried to solve:

let x be the number of slice of cake and y be the number of drink.

2x+y=1
so 8 person 8(2x+8y)=8

500(x/2)+220y=7000 or 500x+200y=7000

however the question is asking for inequalities and i could not found the correct equation. Please advise.

Thank you

I don't see that the question is explicitly "asking for inequalities"; did you omit something, or is that just how you interpret "possible"?

In any case, your equation doesn't make sense; if 2x+y=1, then x and y are either fractions, negative, or both! Why would twice the number of slices plus the number of drinks equal 1?

The question isn't clear to me, but perhaps it means that you need at least enough slices for two per person, and at least enough drinks for 1 per person. The smallest number of drinks would be 1 per person; the largest would be when there are the minimum number of cakes. That gives you an inequality.

 

[Amb]

I don't see that the question is explicitly "asking for inequalities"; did you omit something, or is that just how you interpret "possible"?

In any case, your equation doesn't make sense; if 2x+y=1, then x and y are either fractions, negative, or both! Why would twice the number of slices plus the number of drinks equal 1?

The question isn't clear to me, but perhaps it means that you need at least enough slices for two per person, and at least enough drinks for 1 per person. The smallest number of drinks would be 1 per person; the largest would be when there are the minimum number of cakes.

I don't see that the question is explicitly "asking for inequalities"; did you omit something, or is that just how you interpret "possible"?

In any case, your equation doesn't make sense; if 2x+y=1, then x and y are either fractions, negative, or both! Why would twice the number of slices plus the number of drinks equal 1?

The question isn't clear to me, but perhaps it means that you need at least enough slices for two per person, and at least enough drinks for 1 per person. The smallest number of drinks would be 1 per person; the largest would be when there are the minimum number of cakes. That gives you an inequality.

The topic for this word problem is inequalities.

I couldn't figure out how to write the equations.

1 cake box has 2 slices of cake. So if 1 slice of cake is x, 2 slices would be 2x and 1 drink is y. So does it mean volume of 2 x + y = 720?

7000/720 is number of sets of 1 cake box and 1 drink?

I don't understand how to work it out

2x+y = 1, 1 what????
What does at least 2 mean to you?

How does 500(x/2)+220y=7000 become 500x+200y=7000?

1 is 1 person? 2 slice of cake is 2x and 1 drink is y.

1 box of 2x is 500 cm cube and 220 of y = 7000?

1 box of 2 slice of cake = 500 cm cube
1 drink = 220 cm cube
8 person needs at least 4000 cm cube and 1760 cm cube of space in package

7000/5760= 175/144= 1.215 (4sf)

Left 1400 cm cube space.

If at least 2 cakes, could I say that x=3?

What is the meaning of [imath]2x+y=1[/imath] ?

Also, check you last line of equations -- you have at lest two typos/mistakes there.

I do not know how to interpret this question so the attempt is my thoughts of how it could be worked out. So I may not know what is the typo

I don't see that the question is explicitly "asking for inequalities"; did you omit something, or is that just how you interpret "possible"?

In any case, your equation doesn't make sense; if 2x+y=1, then x and y are either fractions, negative, or both! Why would twice the number of slices plus the number of drinks equal 1?

The question isn't clear to me, but perhaps it means that you need at least enough slices for two per person, and at least enough drinks for 1 per person. The smallest number of drinks would be 1 per person; the largest would be when there are the minimum number of cakes. That gives you an inequality.

The topic for this question is inequalities

 

[blamocur]

1 box of 2 slice of cake = 500 cm cube
1 drink = 220 cm cube
8 person needs at least 4000 cm cube and 1760 cm cube of space in package

7000/5760= 175/144= 1.215 (4sf)

Left 1400 cm cube space.

If at least 2 cakes, could I say that x=3?

I am not sure what the problem statement means. The way I interpret it is "what is the maximum possible number of drinks which satisfies the requirement of 2 slices and 1 drink per person". In this interpretation once you satisfy the minimal requirement you still have 1400 cm^3 left -- how many additional drinks can you fit in there ?

 

[Dr.Peterson]

1 box of 2 slice of cake = 500 cm cube
1 drink = 220 cm cube
8 person needs at least 4000 cm cube and 1760 cm cube of space in package

7000/5760= 175/144= 1.215 (4sf)

Left 1400 cm cube space.

If at least 2 cakes, could I say that x=3?

One thing you have found here (without quite saying it) is that each person needs 720 cm³ for their minimum, and the 8 together need 5760 cm³. That's good.

But how much space does that leave for extra food? It isn't 1400 cm³. Where did you get that?

Now, what is the smallest number of drinks that can be put in that space? (Easy!)

And what is the largest number of drinks that can fit? (A little harder.)

Then write an inequality that says this.

You could possibly do this by solving an inequality for a variable, but it doesn't seem necessary to me.

 

[Steven G]

2 slice of cake is 2x and 1 drink is y.
If that's true then all is easy.

2 slices of cake = 2x. Divide by 2. Then 1 slice of cake = x, that is x = 1 slice of cake.

1 drink = y or y=1 drink.

Either the answer is x = 1 slice of cake and y = 1 drink or you defined your variables incorrectly.

 

[blamocur]

One thing you have found here (without quite saying it) is that each person needs 720 cm³ for their minimum, and the 8 together need 5760 cm³. That's good.

But how much space does that leave for extra food? It isn't 1400 cm³. Where did you get that?

Now, what is the smallest number of drinks that can be put in that space? (Easy!)

And what is the largest number of drinks that can fit? (A little harder.)

Then write an inequality that says this.

You could possibly do this by solving an inequality for a variable, but it doesn't seem necessary to me.

Wish I've noticed that

 

[Amb]

One thing you have found here (without quite saying it) is that each person needs 720 cm³ for their minimum, and the 8 together need 5760 cm³. That's good.

But how much space does that leave for extra food? It isn't 1400 cm³. Where did you get that?

Now, what is the smallest number of drinks that can be put in that space? (Easy!)

And what is the largest number of drinks that can fit? (A little harder.)

Then write an inequality that says this.

You could possibly do this by solving an inequality for a variable, but it doesn't seem necessary to me.

Oops it should be 1240.

Yes doing it without inequalities I would just need to divide the rest by 220.

I am stumped by the part at least 2 sandwiches.

 

[Amb]

Thanks for your help. I reckon that I should solve without inequalities. It is much easier that way.

Answer I got is 13

 

[Dr.Peterson]

Oops it should be 1240.

Yes doing it without inequalities I would just need to divide the rest by 220.

I am stumped by the part at least 2 sandwiches.

Where does the problem mention sandwiches? Did you not state the entire problem, or did the cake transmute?

John is packing a package for 8 people (including himself). He wants each person to have at least 2 slices of cakes and 1 drink. Each cake box containing 2 slices of cakes has a volume of 500 cubic centimeter and 1 drink has a volume of 220 cubic centimeters. If the package can hold a volume of 7 litres, find the possible number of drinks in the package.