Question

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?

Answer 1

Answer:

          $\large\boxed{\large\boxed{\text{54 lattes were sold}}}$

Explanation:

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

1. Name the variables:

• L: number of lattes

• C: numberof cappuccinos

2. First equation:

• Lattes for $4 ⇒ sale from L lattes = 4L

• Cappuccinos for $3. ⇒ sale fro C cappuccinos = 3C

• Last 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= 252

• Add like terms: 24 + 19C = 252

• Subtraction property of equalities: 19C = 252 - 24

• Do the operation: 19C = 228

• Division property of equalities:  C = 228 / 19

• Do the operation: C = 12

Subsitute C = 12 in L = 6 + 4C

• L = 6 + 4(12) = 6+ 48 = 54

Answer: 54 lattes were sold