Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Mrs. Kirk sometimes makes her melon salad for special events. When she made it a couple months ago, she used 1 kilogram of honeydew melon and 2 kilograms of watermelon, which cost her $7. Today, she used 3 kilograms of honeydew melon and 3 kilograms of watermelon, spending a total of $15 on the melons. Assuming that the prices of the melons haven't changed, how much does a kilogram of each type of melon cost?

Answer 1

Given that 1 kilogram of honeydew melon and 2 kilograms of watermelon, which cost her $7 and 3 kilograms of honeydew melon and 3 kilograms of watermelon, spending a total of $15 on the melons

Let x be the cost of a kilogram of honeydew melon and y be the cost of a kilogram of watermelon.

The system of equation is

`x+2y=7\text{ take this as equation (1).}`

`3x+3y=15\text{ take this as equation (2).}`

Multiply equation (1) by 3, we get

`3* x+3*2y=3*7`

`3x+6y=21\text{ take this as equation (3 ).}`

Subtracting equation (2) from equation (3), we get

`(3x+6y)-(3x+3y)=21-15`

`3x+6y-3x-3y=6`

`3y=6`

Dividing by 3, we get

`(3y)/(3)=(6)/(3)`
`y=2`

Substitute y=2 in equation (1), we get

`x+2*2=7`

`x+4=7`

Subtracting 4 from both sides, w get

`x+4-4=7-4`
`x=3`

The cost of a kilogram of honeydew melon =$ 3.

The cost of a kilogram of watermelon = $ 2.