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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beckden's profile pic

beckden | High School Teacher | (Level 1) Educator

Posted on

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.

beckden's profile pic

beckden | High School Teacher | (Level 1) Educator

Posted on

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.

brucebanner's profile pic

brucebanner | Student, Undergraduate | eNotes Newbie

Posted on

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

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