Question

Juice-O-Rama is a refreshment stand specializing in a fruit drink mixture of orange juice and prune juice. The orange juice costs $1.20 per liter and the prune juice costs $1.40 per liter. If they need 8 liters of the final drink at a cost of $1.24 per liter, how many liters of each juice will they need to make their specialty drink?

Answer 1

Hi there. Did you just want an answer or do you want to learn the material?

Answer 2

I want to learn. I dont understand.

Answer 3

OK. So call 'x' the number of liters of orange juice, and 'y' the number of liters of prune juice'. We need to write two equations that relate X to Y.

First, we need a total of 8 liters of juice. so, how can you write this in terms of X and Y?

Answer 4

x+y=8

Answer 5

yes!. nice. And, we want the total cost to be 1.24 per liter. So let's do this equation step by step. If it costs 1.24 per liter and we want 8 liters, what's the total cost?

Answer 6

1.24(8) = 9.92

Answer 7

yep. And, the total cost is equal to the sum of the cost of the orange juice and the cost of the prune juice. so if we have X liters of orange, and Y liters of prune, how much does the total cost, given the cost per liter of each juice in the problem?

Answer 8

this is where i am lost.

Answer 9

ok. How much is orange juice per liter?

Answer 10

1.20

Answer 11

and we have X liters of it. So in the final mixture, there is how much worth of orange juice in it?

Answer 12

1.20x+1.40y=9.92?

Answer 13

you got it my friend. that's our second equation. now solve that simultaneously with the first, x+y=8

Answer 14

we have X liters of OJ, and Y liters of prune, and the total value of the 8 liters is 9.92.

Answer 15

how do i solve it?

(-1) x+y=8
-x-y=-8?

Answer 16

for this one the substitution method is probably easier than the addition method, i.e.
x+y=8
x = 8-y

then substitute x=8-y into equation 2.

Answer 17

x=6.4 y =1.6

Answer 18

?

Answer 19

that's what I got!

Answer 20

Thank You so much. I just have one question. How do I know when to use the addition method vs. the substitution method.

Answer 21

Honestly, whichever looks easier to you. Both methods are guaranteed to give you the same answer, but sometimes one has easier math than the other. I picked substitution method for that one because I could express x without a fraction. Fractions always make the math harder.

If there's something like this:

2x + 8y = 3
2x - 3y = 7

Then I'll usually use the addition method because trying to isolate x or y in either of those equations would result in ugly fractions, whereas I can see easily that just reversing the sign of the second equation and adding gives me 11y = 10.

Answer 22

thank you!

Answer 23

Oops, I mean 11y = -4.... ha. I'm not good at math ;-)