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

Answer:

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

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

Step-by-step 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 $\times$ total gallons

$=x\times3\\=3x$

Jeremiah bought $4$ container of strawberries

So total spend on = strawberries =cost pf $1$ container $\times$ total container

$=y\times4\\=4y$

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 = $5\times x=5x$

Gary bough $2$ containers of strawberries

so total spend on strawberries = $2\times y=2y$

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)

$(10x-3x)+(4y-4y)=(44-19.50)\\\\7x=24.5\\\\x=\frac{24.5}{7}\\\\x=3.5$

Substitute in eqn(2)

$5\times3.5+2y=22\\\\2y=22-5\times3.5=22-17.5\\\\2y=4.5\\\\y=\frac{4.5}{2}\\\\y=2.25$

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

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