Question

The values of two antiques were observed for a period of 50 years. The following equations model the value of each antique, where y is the value of the antiques and x is the number of years after observations began. Antique 1: y=−x^2+50x Antique 2: y= 10x+175 Determine when the two antiques had the same value. Select all that apply.
a. After 5 years
b. After 40 years
c. After 35 years
d. After 50 years

Answer 1

Hello,

y=10x+175
y=-x²+50x

==> x²+10x-50x+175=0
==>x²-40x+175=0
==>x²-5x-35x+175=0
==>x(x-5)-35(x-5)=0
==>(x-5)(x-35)=0
==> x=5 or x=35

Answer:  A AND C.