# How do I find the answer to this question? 4 unknowns, only 3 equations, some people said there's no way to do it, but my teacher says there is a way.Jamie bought 1 pound of Jolly Ranchers and 2...

How do I find the answer to this question? 4 unknowns, only 3 equations, some people said there's no way to do it, but my teacher says there is a way.

Jamie bought 1 pound of Jolly Ranchers and 2 pounds of mints for $2.00. The next week, he bought 4 pounds of lollipops and 1 pound of Jolly Ranchers for $3.00. The next week, he bought 3 pounds of Skittles, 1 pound of Jolly Ranchers, and 1 pound of lollipops for $1.50. How much would he have to pay on his next trip to the candy store if he bought 1 pound of each of the 4 kinds of candy?

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### 3 Answers

I fingured out a more analytic method.

First use (2) to solve for J we get

J = 3 - 4L

Substitute this into (3) we get

3S + 3 - 4L + L = 1.5

SImplify

3S - 3L = -1.5

Solve for L we get

L = S + 0.5

Now substitute this into (2)

4(S + 0.5) + J = 3

4S + 2 + J = 3

Solve for J we get

J = 1 - 4S

Now substutute this into (1) and solve for M

1 - 4S + 2M = 2

2M = 4S + 1

M = 2S + 0.5

Now we add these together

J + L + M = 1-4S + S+0.5 + 2S+0.5

Simplify the right and we get

J + L + M = 2 - S

Add S to both sides and we get

J + L + M + S = 2

So the answer is the 4 candies at 1lb each cost $2.00

We can also put some constraints on these numbers. All candies cost more than $0 (we assume) and all are less than $2.00. Since J = 1-4S,

S has to be less than 0.25 otherwise J would not be positive.

J is less than $1/lb.

L is less than $0.75/lb.

M is less than $1/lb.

You are correct, you will not be able to solve for one variable, but we can manipulate the equations to get the total cost of 1lb each of the candies.

I am not sure if there is a method here, I played with the equations until I got a sum of the 4 candies. Sorry I do not have a clear process to get this answer. I will look at it and see if I can find one.

J=cost of 1 lb of Jolly Ranchers

M=cost of 1lb of mints

S=cost of 1lb of Skittles

L=cost of 1lb of lollypops

(1) J+2M=2

(2) 4L+J=3

(3) 3S+J+L=1.5

(4) 3J+6M=6 (Multiply (1) by 3)

(5) 6S+2J+2L=3 (Multiply (3) by 2)

(6) 6S+5J+2L+6M=9 (Add (4) and (5))

6S+6J+6L+6M=12 (Add (6) and (2))

Now divide by 6 and we get

S + J + L + M = 2

So the answer is the 4 candies cost at 1lb each cost $2.00.

The answer is 4 candies where 1 candy costs $2. Nice question. I think this will improve people's thinking ability.