Help me with this question please

Question

A company manufactures helmets and bats. They sell six times as many bats as helmets. If they make a profit of $3 per bat and $5 per helmet, how many bats and helmets were sold if the company earned $46,000?

Answer 1

Number of bats = b

Number of helmets = h

Write the information in equations:

 

b = 6h

$3b + $5h = $46000

 

Substitute for b:

 

$3(6h) + $5h = $46000

$18h + $5h = $46000

$23h = $46000

h = $46000/$23 = 2000

 

Solve for b:

 

b = 6h = 6(2000) =12,000

 

CHECK:

 

$3(12,000) + $5(2000) = $36,000 + $10,000 = $46,000.  It checks.

 

Answer: 12,000 bats and 2,000 helmets.

 

Carl