Question

A store is having a sale on jelly beans and trail mix. For 5 pounds of jelly beans and 3 pounds of trail mix, the total cost is $20. For 7 pounds of jelly beans and

9 pounds of trail mix, the total cost is $46. Find the cost for each pound of jelly beans and each pound of trail mix.
Cost for each pound of jelly beans:
Cost for each pound of trail mix:

Answer 1

Cost for each pound of jelly beans: $1.75

Cost for each pound of trail mix: $3.75

Explanation:

Define the variables:

• Let J be the cost of one pound of jelly beans.
• Let T be the cost of one pound of trail mix.

Using the given information and defined variables, create a system of equations:

`\begin{cases}5J+3T=20\\7J+9T=46\end{cases}`

To solve the system of equations, multiply the first equation by 3 to create a third equation:

`5J \cdot 3+3T \cdot 3=20\cdot 3`

`15J+9T=60`

Subtract the second equation from the third equation to eliminate the term in T:

`\begin{array}{crcrcl}&15J & + & 9T & = & 60\\\vphantom{\frac12}- & (7J & + & 9T & = & 46)\\\cline{2-6}\vphantom{\frac12} &8J&&&=&14\end{array}`

Solve the equation for J by dividing both sides by 8:

`(8J)/(8)=(14)/(8)`

`J=1.75`

Therefore, the cost of each pound of jelly beans is $1.75.

To find the cost of one pound of trail mix, substitute the found value of J into one of the original equations and solve for T.

Using the second equation:

`7(1.75)+9T=46`

`12.25+9T=46`

`12.25+9T-12.25=46-12.25`

`9T=33.75`

`(9T)/(9)=(33.75)/(9)`

`T=3.75`

Therefore, the cost of each pound of jelly beans is $3.75.

Answer 2

1 pound of jelly beans cost $1.75 , 1 pound of trail mix cost $3.75

Explanation:

let j represent 1 pound of jelly beans and t represent 1 pound of trail mix , then

5j + 3t = 20 → (1)

7j + 9t = 46 → (2)

multiplying (1) by - 3 and adding to (2) will eliminate t

- 15j - 9t = - 60 → (3)

add (2) and (3) term by term to eliminate t

(7j - 15j) + (9t - 9t) = 46 - 60

- 8j + 0 = - 14

- 8j = - 14 ( divide both sides by - 8 )

j =
`(-14)/(-8)` = 1.75

substitute j = 1.75 into either of the 2 equations and solve for t

substituting into (1)

5(1.75) + 3t = 20

8.75 + 3t = 20 ( subtract 8.75 from both sides )

3t = 11.25 ( divide both sides by 3 )

t = 3.75

then

cost of 1 pound of jelly beans = $1.75

cost of 1 pound of trail mix = $3.75