A coffee shop sells lattes for $4 and cappuccinos for $3. Last Friday, the sales totaled $252. If the number of lattes sold was 6 more than 4 times the number of cappuccinos, how many lattes were sold?

         

Explanation:

This is a typical problem to solve with a system of two linear equations.

1. Name the variables:

L: number of lattesC: numberof cappuccinos

2. First equation:

Lattes for $4 ⇒ sale from L lattes = 4L Cappuccinos for $3. ⇒ sale fro C cappuccinos = 3CLast Friday, the sales totaled $252 ⇒ 4L + 3C = 252

First equation: 4L + 3C = 252

3. Second equation:

The number of lattes sold was 6 more than 4 times the number of cappuccinos ⇒L = 6 + 4C

Second equation: L = 6 + 4C

4. Solve the system:

Substitute L on the first equation with 6 + 4C

4 (6 + 4C) + 3C = 252

Solve:

Distributive property: 24 + 16C + 3C= 252Add like terms: 24 + 19C = 252Subtraction property of equalities: 19C = 252 - 24Do the operation: 19C = 228Division property of equalities:  C = 228 / 19Do the operation: C = 12

Subsitute C = 12 in L = 6 + 4C

L = 6 + 4(12) = 6+ 48 = 54

54 lattes were sold