Question

Michael spent $18 at a local farmers’ market. The apples he bought cost $2 per pound, and the peppers cost $3 per pound. How many pounds of apples and peppers did he buy?

This equation represents the scenario:

2a + 3p = 18

Choose the equations that are equivalent.
Check all that apply.
p = two-thirds a + 6
p = negative two-thirds a + 6
a = negative 1 and one-half p + 9
a = 1 and one-half p + 9
a = StartFraction negative 3 p + 18 Over 2 EndFraction

Answer 1

p = -2/3a +6

a = -3/2 p +9

a = -1 1/2 p +9

a = (-3p+18)/2

Explanation:

2a + 3p = 18

Solve for a

2a +3p -3p = 18-3p

2a = 18 -3p

Divide by 2

a = 18/2 - 3p/2

a = 9 - 3/2 p

a = -3/2 p +9

a = -1 1/2 p +9

a = (-3p+18)/2

Solve for p

2a +3p = 18

3p = 18 -2a

Divide by 3

p = 18/3 - 2/3 a

p = 6 -2/3a

p = -2/3a +6