word problem

T

Thank you Sal

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André, Bruno and Carlos went out for pizza. André ate 1/4 of the pizza, Bruno
ate 1/3 and Carlos ate 1/5. They then decided that the restaurant bill would be
divided into parts directly proportional to the pizza consumption of each of the
friends.
Knowing that the three friends spent 94$ calculate the amount paid by André.

My attempt
andre ate 1/4
pizza = 94 94/4 = 23.5$

But aperently the right answer is listed as 30$. I cant think of any equation or any other way that would get me to that answer
 
Thank you Sal said:
André, Bruno and Carlos went out for pizza. André ate 1/4 of the pizza, Bruno
ate 1/3 and Carlos ate 1/5. They then decided that the restaurant bill would be
divided into parts directly proportional to the pizza consumption of each of the
friends.
Knowing that the three friends spent 94$ calculate the amount paid by André.

My attempt
andre ate 1/4
pizza = 94 94/4 = 23.5$

But aperently the right answer is listed as 30$. I cant think of any equation or any other way that would get me to that answer
Click to expand...
Here's a simpler problem that may help.
3 friends bought 4 apples for $4. They ate one apple each. They decided the bill would be divided into parts directly proportional to the apple consumption. How much did each one pay?
 
Your answer would be correct if the three ate the entire pizza. 1/4 + 1/3 + 1/5 is Not 1. So the three have to split the price for the cost of the pie that was not eaten proportional to what part of the pizza each person ate.
Note that 94/4 + 94/3 + 95/5 is not 94!
 
4 apples = 4 $
1 apple = 1 $
A, B and C ate 1 apple, so each will spend 1 dollar + value of the apple no one ate, equaly split betwen them
A B C = 1 + 1 divided by 3
ABC = 1.3(insert viniculum) -> Each will pay ≈1.3 Dollars

Solving this problem gave me a better understanding about it, it made the structure clearer
Now I feel more confident to tackle the pizza problem, I'll post it as soon as I finish it as a token of my appreciation.
 
4 apples = 4 $
1/4 + 1/3 + 1/5 = 94$
15/60 + 20/60 + 12/60 = 94$
47/60 = 94$

From here I found 2 possible ways, (sorry if its confusing)

Way 1 Way2
slices eaten-----> 47 = 94$ <-Price for 60 slices
------------------> ---
total slices paid-> 60		(47/60)*60/47 = 94*60/47
(multiplying both sides by the reciprocal of 47/60 so that we can know the cost of 1 piece is)
price per slice = 94/60 -> 1.56$1=5,640/47
Slices not eaten = 13 (amount to be payed equaly because no one ate)1=120
slices eaten-> 15 20 12 <> 1 1 1
--------------> --- --- --- = -- -- -- = Andre Bruno Carlos
total slices---> 60 60 60 <> 4 3 5
how much did andre pay?
his 15 slices + equal pay of non eaten slices = 13/3
15 * 1.56$ + (13*1.56)/3
23.4 + 6.76 = 30.16 ≈ 30$
--------------------------------------------------------------------
Way 2
Andre ate 1/4 of the piece so what did he pay?
1=120$
1/4=120$/4
1/4 = 30$
(although in this way i cannot tell why I do not have to add the non eaten slices)

Big thanks to Iev888 for helping me and others out! as well as Jomo and all you guys that gracefully give your time for what I consider a noble task.
 
Last edited:
Thank you Sal said:
4 apples = 4 $
1 apple = 1 $
A, B and C ate 1 apple, so each will spend 1 dollar + value of the apple no one ate, equaly split betwen them
A B C = 1 + 1 divided by 3
ABC = 1.3(insert viniculum) -> Each will pay ≈1.3 Dollars

Solving this problem gave me a better understanding about it, it made the structure clearer
Now I feel more confident to tackle the pizza problem, I'll post it as soon as I finish it as a token of my appreciation.
Click to expand...
Looks good. But can you solve it in a way that can be applied to your problem? I.e. don't take advantage of the convenient numbers. Maybe set up and solve an equation.
 
Thank you Sal said:
Intended format->
View attachment 30088
Click to expand...
Pretty confusing.
Here's how I would solve the apples problem.
Proportions of apple consumption: 1:1:1
Therefore, the payment can be represented as:
1x + 1x + 1x = $4.
3x = 4
x = $1.33
1x = $1.33 - that's what each one paid.

Can you apply this method to your problem?
 
Thank you Sal said:
André, Bruno and Carlos went out for pizza. André ate 1/4 of the pizza, Bruno
ate 1/3 and Carlos ate 1/5. They then decided that the restaurant bill would be
divided into parts directly proportional to the pizza consumption of each of the
friends.
Knowing that the three friends spent 94$ calculate the amount paid by André.

My attempt
andre ate 1/4
pizza = 94 94/4 = 23.5$

But aperently the right answer is listed as 30$. I cant think of any equation or any other way that would get me to that answer
Click to expand...
Proportion of Pizza consumed → 15:20:12 → 15+20+12 = 47

Amount of payment → 15*94/47 : 20 * 94/47 :12 * 94/47 → 30 : 40 : 24 [ check 30+40+24 = 94 = given total]

That is one expensive pizza!!
 
Last edited by a moderator:
lev888 said:
Can you apply this method to your problem?
Click to expand...
Proportion of pizza consumption: 1/4 : 1/3 : 1/5
1x/4 + 1x/3 + 1x/5 = 94$ ( if you eat 1/4 of pizza that has x slices + 1x/3 + 1x/5 = 94$)
15x/60 + 20x/60 + 12x/60 = 94$
47x/60 =94$
(94*60)/47=x
120=x
120 is the total pizza slices
A 120*1/4 = 30 ( A ate 30 pizza slices)
B 120*1/3 = 40 ( B ate 40 pizza slices)
C 120*1/5 = 24 ( C ate 24 pizza slices)
Figuring out how much does 1 slice cost
30x+40x+24x=94 -> 94x=94 -> x=1 -> 1 slice = 1$
A had 30 slices that cost 1$ -> 30*1$= 30$ -> A spent 30$
(Recap: total parts = 120, cost per part = 1, ratio of total consumed parts = 1/4 : 1/3 : 1/5 )

This method enables the discovery of a variable (x) that needs to be multiplied by the ratio : of each individual to reveal thei'r consumption.
This method works way better than the others iv'e tried, thanks again for sharing!.
 
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