Question

Valeria is ordering medals for her school's track meet. Company A charges $4.50 for each medal and a one-time engraving fee of$40. Company B charges $6.50 for each medal and a one-time engraving fee of $20. Which inequality can be used to find x, theleast number of medals that can be ordered so that the total charge for Company A is less than the total charge for Company B?esA)4.5+ 40x<6.5 + 20xB)4.5+ 40x > 6.5 + 20xo4.5x + 40 < 6.5x + 20D)4.5x + 40 > 6.5x + 20

Answer 1

We will determine the inequality as follows:

*First: We will determine the interception point of the two equations, that is:

`y=4.50x+40`
`y=6.50x+20`

So:

`4.50x+40=6.50x+20\Rightarrow4.50x-6.50x=20-40`
`\Rightarrow-2x=-20\Rightarrow x=10`

Now, we replace x = 10 on any of the two equations:

`y=4.50x+40\Rightarrow y=4.50(10)+40`
`\Rightarrow y=45+40\Rightarrow y=85`

So, the interception point is located at (10, 85).

*Second: We determine the inequality that represents the problem, that is:

`6.50x+20>4.50x+40`

[This is overall, the second equation represents greater cost].

*Third: The least number of medals that cab ve ordered so company's A cost is less than company's B cost is 10 medals.