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?
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
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
(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.