Question

Jeremiah bought three gallons of ice cream and four containers of strawberries for $19.50. Gary bought five gallons of ice cream and two containers of strawberries for $22. What is the cost of one gallon of ice cream? What is the cost of one container of strawberries?

Answer 1

Cost of
`1` gallon of ice cream
`=\$3.5`

Cost of
`1` container of strawberries
`=\$2.25`

Explanation:

Let cost of
`1` gallon ice cream
`=\$x`

Let cost of
`1` container of strawberries
`=\$y`

Jeremiah's purchase

Jeremiah bought
`3` gallon of ice cream

so total spend on ice cream = cost of
`1` gallon
`*` total gallons

`=x*3\\=3x`

Jeremiah bought
`4` container of strawberries

So total spend on = strawberries =cost pf
`1` container
`*` total container

`=y*4\\=4y`

Jeremiah's total expenditure
`=\$19.50`

`3x+4y=19.50 .......(1)`

Gary's purchase

Gary bought
`5` gallons of ice cream

so total spend on ice cream =
`5* x=5x`

Gary bough
`2` containers of strawberries

so total spend on strawberries =
`2* y=2y`

Gary's total expenditure
`=\$22`

`5x+2y=22.....(2)`

solve eqn(1) and eqn(2)

`3x+4y=19.50\\5x+2y=22`

multiply eqn(2) by (2) and eqn(2)-eqn(3)

`(10x-3x)+(4y-4y)=(44-19.50)\\\\7x=24.5\\\\x=(24.5)/(7)\\\\x=3.5`

Substitute in eqn(2)

`5*3.5+2y=22\\\\2y=22-5*3.5=22-17.5\\\\2y=4.5\\\\y=(4.5)/(2)\\\\y=2.25`

Cost of
`1` gallon of ice cream
`=\$3.5`

Cost of
`1` container of strawberries
`=\$2.25`