Question

A manufacturing company spends $1200 each day on plant costs plus $7 per item for labor and materials. The items sell for $23 each. How many items must the company sell in one day to equal its daily costs?

Answer 1

Company must sell 75 items to match the daily costs.

Explanation:

Let
`x` be the number of items the company must sell to match the daily costs.

Money spent each day on plant =
`\$1200`

Money spent on labor and materials on each item =
`\$7`

Money spent on labor and materials on
`x` items =
`\$7x`

Total money spent or total cost =
`1200 + \$7x ...... (1)`

Sales price for 1 item =
`\$23`

Sales price for
`x` items =
`$23x ...... (2)`

Equating the equation (1) and (2) so that the company can match the daily costs with sales price:

`\Rightarrow 1200 + 7x = 23x\\\Rightarrow 16x = 1200\\\Rightarrow x = 75`

Company must sell 75 items to match the daily costs.