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

$3\times x+3\times2y=3\times7$

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

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

$\frac{3y}{3}=\frac{6}{3}$$y=2$

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

$x+2\times2=7$

$x+4=7$

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.