Question

Today a bakery sold 90 cupcakes and 60 doughnuts. The number of cupcakes sold has been increasing by 6 every day. Consequently, the number of doughnuts sold has been decreasing by 8 everyday. How many days will it be until the number of cupcakes sold is three times the number of doughnuts sold?

Answer 1

3 days

Explanation:

Cupcakes: 90 + 6d

Increasing by 6 each day

Doughnuts: 60 -8d

Decreasing by 8 each day

We want the number of cupcakes sold to equal = 3 times the number of doughnuts sold. Take the expression for cupcakes and set it equal to 3 times the expression for doughnuts

90 + 6d = 3( 60-8d)

Distribute

90 + 6d = 180 - 24d

Add 24d to each side

90 +6d +24d = 180-24d +24d

90 + 30d = 180

Subtract 90 from each side

90-90 +30d = 180 -90

30d = 90

Divide by 30

30d/30 = 90/30

d =3