Question

I NEED HELP!! An energy bar company manufactures peanut butter and chocolate bars.
Peanut butter bars cost 25¢ per lb.
The chocolate bars cost 30¢ per lb.
The company sold 260 lbs of bars for $71.
How many of the bars sold were peanut butter?

Answer 1

You need a system of equations to figure this out. You need to relate the number of bars sold to each other as the first equation, then you would need to relate the money they cost and how much money they made as the second equation.

Answer 2

i got this equation.....25x+(260-x)30=71

Answer 3

Call pounds of pb bars p; call pounds of chocolate bars c. pounds of pb bars + pounds of chocolate bars = 260 pounds. That's the first equation.

Answer 4

p+c=260

Answer 5

Next relate the money in a second equation.

Answer 6

so 25p+(260-p)30c=71

Answer 7

pb costs .25 per pound and c costs .30 per pound and there is a total of $71 made. Convert either the cents to dollars or the dollars to cents so you are working in only one denomination of money.

Answer 8

We now have that .25pb + .30c = 71

Answer 9

That's our second equation.

Answer 10

p + c = 260
.25p + .30c = 71

Answer 11

.25pb+.30c=71 is second

and were trying to find the first

Answer 12

Solve them simultaneously. You could use substitution for c; p = 260-c.

Answer 13

yeah but how are we going to find the first equation

Answer 14

Ok, let's do this step by step. We related the numbers of pounds of bars in our first equation, which was
p + c = 260

Answer 15

Our second equation relating the cost per pound and the money they made is
.25p + .30c = 71

Answer 16

yes

Answer 17

right

Answer 18

We need to solve these at the same time, using one to solve the other. If we use substitution we can eliminate one variable. From the first equation,
p + c = 260
we can solve for p to get rid of c like this:
p = 260 - c

Answer 19

Now we have a "new value" for p that we can sub into our second equation to get that equation into terms of only p and no c. Like this:

Answer 20

ok

Answer 21

.25p + .30c = 71
.25(260-c) + .30c = 71
I meant "no p only c" When we do this we are eliminating the problem of 2 variables. We get rid of the p and only need to worry about c.

Answer 22

p = 260 - c, so we sub 260 - c in for p.

Answer 23

(260)p+c=

Answer 24

.25(260-c) + .30c = 71
.25 * 260 = 65....25 * -c = -.25c
65 - .25c + .30c = 71
is what we have now.

Answer 25

Not just 260, it's "260 - c" that is equal to p. When we see the p in our second equation we need to replace it with 260-c. No more p then.

Answer 26

gotchu

Answer 27

65 - .25c + .30c = 71

We can now solve that for c. Can you do that?

Answer 28

Combine the c terms on one side of the equals sign and the numbers on the other side of the equals sign.

Answer 29

.55c

Answer 30

65-.55c=71

Answer 31

it's not .30c + .25c, it's .30c - .25c

Answer 32

then it would be 0.05

Answer 33

.30c - .25c = .05c You added the .25c and it's supposed to be subtracted.

Answer 34

yes....05c. Go on...

Answer 35

You now have .05c = 71-65 which is...

Answer 36

.05c = ?

Answer 37

.05c=6

Answer 38

Good! Now solve for c. What do you get?

Answer 39

120

Answer 40

unless its a frction, in that case it would be 6/.05

Answer 41

Good! Verry good! That tells us that there was 120 pounds of chocolate bars sold. The total amount in pounds of chocolate and pb is 160. If we know that 120 pounds of chocolate was sold and the total pounds of pb + c = 160, and c = 120, then pb + 120 = 160. How do you solve for pb now?

Answer 42

wouldnt it be 40?

Answer 43

160-120=40

Answer 44

good...120 chocolate and 40 pb. that's your answer!

Answer 45

thank you so much for the help