Question

Jennifer's bill for 6 cans of grape juice and 4 cans of apple juice was $13.10. When she got home she found out that she should have bought 4 cans of grape juice and 6 cans of apple juice. Although she mixed up the order, she did save 60 cents. What is the cost per can of apple and grape juice

Solve the problem using substitution and elimination.
Convert your equations to slope intercept form and identify the variables for your x and y axes. Then graph.
SHOW ALL WORK

Answer 1

Part 1) The system is solved using elimination

The cost per can of grape juice is
`\$1.19` and the cost per can of apple juice is
`\$1.49`

Part 2) The system is solved using substitution

The cost per can of grape juice is
`\$1.19` and the cost per can of apple juice is
`\$1.49`

Part 3) The system is solved by graphing

The graph in the attached figure

Explanation:

Part 1) Solve the system by elimination

Let

x----> the cost per can of grape juice

y----> the cost per can of apple juice

we know that

`6x+4y=13.10` -----> equation A

`4x+6y=13.10+0.60`

`4x+6y=13.70` -----> equation B

Solve the system by elimination

Multiply the equation A by -6 both sides

`-36x-24y=-78.6` -------> equation C

Multiply the equation B by 4 both sides

`16x+24y=54.8` -------> equation D

Adds equation C and equation D

`-36x-24y=-78.6\\16x+24y=54.8\\----------\\-36x+16x=-78.6+54.5\\-20x=-23.8\\x=1.19`

Substitute the value of x in the equation A

`6(1.19)+4y=13.10`

`4y=5.96`

`y=1.49`

therefore

The cost per can of grape juice is
`\$1.19`

The cost per can of apple juice is
`\$1.49`

Part 2) Solve the system by substitution

Let

x----> the cost per can of grape juice

y----> the cost per can of apple juice

we know that

`6x+4y=13.10`

`4y=-6x+13.10`

`y=-1.5x+3.275` -----> equation A

`4x+6y=13.10+0.60`

`4x+6y=13.70`

`6y=-4x+13.70`

`y=-(4/6)x+13.70/6`

`y=--0.67x+2.28` -----> equation B

Substitute equation B in equation A and solve for x

`-0.67x+2.28=-1.5x+3.275`

`1.5x-0.67x=3.275-2.28`

`0.83x=0.995`

`x=1.19`

Find the value of y

Substitute the value of x in the equation A

`y=-1.5(1.19)+3.275=1.49`

therefore

The cost per can of grape juice is
`\$1.19`

The cost per can of apple juice is
`\$1.49`

Part 3) Solve the system by graphing

we have

`y=-1.5x+3.275` -----> equation A

`y=-(4/6)x+13.70/6` -----> equation B

Remember that

The solution of the system of equations is equal to the intersection point both lines

The solution is the point
`(1.19,1.49)`

see the attached figure

therefore

The cost per can of grape juice is
`\$1.19`

The cost per can of apple juice is
`\$1.49`