Math Is Fun Forum

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Reducing Size of Candy Bar

A jumbo chocolate bar with rectangular shape measures 12 cm in length, 7 cm in width, and 3 cm in thickness. Due to escalating costs of cocoa, management decides to reduce the volume of the bar by 10%. To accomplish this reduction, management decides that the new bar should have the same 3 cm thickness, but the length and width of each should be reduced an equal number of centimeters. What should be the dimensions of the new candy bar?

This one through me into a loop.
I think this problem demands the use of the volume formula
V = length • width • height. The part about reducing the volume by 10% is confusing to me.

Can someone explain what is going on in this problem and set up the right equation for me to use?

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Reducing Size of Candy Bar

A jumbo chocolate bar with rectangular shape measures 12 cm in length, 7 cm in width, and 3 cm in thickness. Due to escalating costs of cocoa, management decides to reduce the volume of the bar by 10%. To accomplish this reduction, management decides that the new bar should have the same 3 cm thickness, but the length and width of each should be reduced an equal number of centimeters. What should be the dimensions of the new candy bar?

This one through me into a loop.
I think this problem demands the use of the volume formula
V = length • width • height. The part about reducing the volume by 10% is confusing to me.

Can someone explain what is going on in this problem and set up the right equation for me to use?

old length: 12
old width: 7
old thickness: 3
old volume: ___

new length: 12 - x
new width: 7 - x
new thickness: 2
new volume: ___

new volume is 90% of old volume

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Reducing Size of Candy Bar

A jumbo chocolate bar with rectangular shape measures 12 cm in length, 7 cm in width, and 3 cm in thickness. Due to escalating costs of cocoa, management decides to reduce the volume of the bar by 10%. To accomplish this reduction, management decides that the new bar should have the same 3 cm thickness, but the length and width of each should be reduced an equal number of centimeters. What should be the dimensions of the new candy bar?

This one through me into a loop.
I think this problem demands the use of the volume formula
V = length • width • height. The part about reducing the volume by 10% is confusing to me.

Can someone explain what is going on in this problem and set up the right equation for me to use?

old length: 12
old width: 7
old thickness: 3
old volume: ___

new length: 12 - x
new width: 7 - x
new thickness: 2
new volume: ___

new volume is 90% of old volume

Old volume = 7•12•3 or 252 cm^3

New volume is 2(12 - x)(7  - 2)

A. Where did 12 come from?

B. Where did 7 come from?

C. What must I do with 90%?

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Reducing Size of Candy Bar

A jumbo chocolate bar with rectangular shape measures 12 cm in length, 7 cm in width, and 3 cm in thickness. Due to escalating costs of cocoa, management decides to reduce the volume of the bar by 10%. To accomplish this reduction, management decides that the new bar should have the same 3 cm thickness, but the length and width of each should be reduced an equal number of centimeters. What should be the dimensions of the new candy bar?

old length: 12
old width: 7
old thickness: 3
old volume: ___

new length: 12 - x
new width: 7 - x
new thickness: 3 (same as old thickness)(sry abt typo before)
new volume: ___

new volume is 90% of old volume

Old volume = 7•12•3 or 252 cm^3

New volume is 2(12 - x)(7  - 2)

this assumes that x=2
how did you get this?
when you checked your ans did it work out right?

A. Where did 12 come from?

B. Where did 7 come from?

A jumbo chocolate bar with rectangular shape measures 12 cm in length, 7 cm in width,, and 3 cm in thickness.

C. What must I do with 90%?

new volume is 90% of old volume
what is 90% of old volume?
set equal and solve

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Reducing Size of Candy Bar

A jumbo chocolate bar with rectangular shape measures 12 cm in length, 7 cm in width, and 3 cm in thickness. Due to escalating costs of cocoa, management decides to reduce the volume of the bar by 10%. To accomplish this reduction, management decides that the new bar should have the same 3 cm thickness, but the length and width of each should be reduced an equal number of centimeters. What should be the dimensions of the new candy bar?

old length: 12
old width: 7
old thickness: 3
old volume: ___

new length: 12 - x
new width: 7 - x
new thickness: 3 (same as old thickness)(sry abt typo before)
new volume: ___

new volume is 90% of old volume

Old volume = 7•12•3 or 252 cm^3

New volume is 2(12 - x)(7  - 2)

this assumes that x=2
how did you get this?
when you checked your ans did it work out right?

A. Where did 12 come from?

B. Where did 7 come from?

A jumbo chocolate bar with rectangular shape measures 12 cm in length, 7 cm in width,, and 3 cm in thickness.

C. What must I do with 90%?

new volume is 90% of old volume
what is 90% of old volume?
set equal and solve

1. I made a typo, obviously.
I meant to say that the new volume is 2(12 - x)(7 -x)

2. The old volume is 252 cm^3. So, 0.90 (252) = 226.8 cm^3.

3. The set up is here:

226.8 = 2(12 - x)(7 - x)

I get two answers for x:

x_1 is approximately-20.67035

We are talking about measurement. So, the value of x_1 must be rejected.

I also know that x_2 is approximately 39.67035. I can round this to be 40.

Dimensions of the new candy bar:

Length = (12 - 40) leads to a negative answer.

Width = (7 - 40) leads to a negative answer.

Height =  2

Something is wrong. The length, width and height must be positive.

What did I do wrong?

Is 226.8 = 2(12 - x)(7 - x) the correct equation needed to find the new length, width and height of the candy bar?

Last edited by sologuitar (2023-11-10 09:43:37)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,190

Re: Reducing Size of Candy Bar

This is my method:

Old volume = 12 times 7 times 3
New volume = (12-x)(7-x) times 3
10% reduction means new volume = 0.9 of old volume. So my equation is

I simplified that to a quadratic, found x and checked it led to a 10% reduction. There was a second value from the quadratic which was obviously too big (ie > 12)

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Reducing Size of Candy Bar

This is my method:

Old volume = 12 times 7 times 3
New volume = (12-x)(7-x) times 3
10% reduction means new volume = 0.9 of old volume. So my equation is

I simplified that to a quadratic, found x and checked it led to a 10% reduction. There was a second value from the quadratic which was obviously too big (ie > 12)

Bob

Wow! You are definitely talented. Trust me, there are thousands of college students and graduate students who have no idea how to even begin solving this problem. I get confused with the bad wording in most word problems. Thanks for the equation. I can take it from here.