Question

Madison is 7 less than four times as old as Paige. The product of their ages is 47 more than the sum of their ages. How old are Madison and Paige?

Answer 1

Step-by-step explanation:

Madison is 7 less than four times as old as Paige. The product of their ages is 47 more than the sum of their ages. How old are Madison and Paige?

• Let M represent Madison and P represent Paige.
• So the first equation will be M = 4 P – 7
• So second equation will be P X M = P + M + 47
• Now substituting for M in the above equation we get
•        P(4P – 7) = P +5 (4P – 7) + 47
•          4 P^2 – 7P = P + 4P – 7 + 47
•         4P^2 – 7P = 5P + 40
•          4P^2 – 12 P – 40 = 0
•            P^2 – 3P – 10 = 0
•            P^2 – 5P + 2P – 10 = 0
•          P(P – 5) + 2(P – 5) = 0
•             (P – 5) (P + 2) = 0
•             P = 5 , - 2  (since age is not negative)
•      So age of Paige is 5  years.
•     Age of Madison will be M = 4P – 7
•                                              = 4(5) – 7
•                                              = 20 – 7
•                                               = 13
• So we have Madison is 13 years old and Paige is 5 years.

Reference link will be

https://brainly.ph/question/2168262

https://brainly.in/question/26552662

Answer 2

Answer:

Madison =13years

Paige =5years

hope it helps you