Question

The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $6500 to rent trucks plus an additional fee of $125.25 for each ton of sugar. The second company charges $5897 to rent trucks plus an additional fee of $175.50 for each ton of sugar. 1)for what amount of sugar do the two companies charge the same ? []tons 2) what is the cost when the two companies charge the same? s[]

Answer 1

The two companies charge the same for 12 tons of sugar.

Amount charged by each of the company
`=\$8003`

Explanation:

Let x denotes amount of sugar for which the two companies charge the same.

Amount charged by the first company
`=6500+125.25x`

Amount charged by the second company
`=5897+175.50x`

To find amount of sugar for which the two companies charge the same,

solve
`6500+125.25x=5897+175.50x`

`6500+125.25x=5897+175.50x\\6500-5897=175.50x-125.25x\\603=50.25x\\x=(603)/(50.25)\\ x=12`

So, the two companies charge the same for 12 tons of sugar.

Amount charged by the first company
`=6500+125.25(12)=8003`

Amount charged by the second company
`=5897+175.50(12)=8003`

Amount charged by each of the company
`=\$8003`