Question

Claire is ordering trophies for her school. Company A charges $4.50 for each trophy and a one-time engraving fee of $26. Company B charges $8.50 for each tu trophy and a one-time engraving fee of $18. Which inequality can be used to find x, the minimum number of trophies than can be ordered so that the total charge at Company A is less than the total charge at Company BA. 4.5 + 26x < 8.5 + 18xB. 4.5 + 26x > 8.5 + 18xC. 4.5x + 26 > 8.5x + 18D. 4.5x + 26 < 8.5x + 18

Answer 1

Company A.

It charges $4.50 per trophy and a one-time fee of $26.

Company B.

It charges $8.50 per trophy and a one-time fee of $18.

To find x where Company A is less than Company B, we form the following inequality.

$4.50x+26<8.50x+18$

Now, we solve for x, first, we have to subtract 8.50 on each side.-

$\begin{gathered} 4.50x+26-8.50x<8.50x+18-8.50x \\ -4x+26<18 \end{gathered}$

Then, we subtract 26 on each side

$\begin{gathered} -4x+26-26<18-26 \\ -4x<-8 \end{gathered}$

At last, we divide the inequality by -4.

$\begin{gathered} -\frac{4x}{-4}>-\frac{8}{-4} \\ x>2 \end{gathered}$

Therefore, the minimum number of trophies that can be ordered so Company A charges less is 3.

The right answer is D.