Question 1137730: What the equation for Jose's age is 7 years more than 3 times Ana's age. If the product of the age is 110, how old is Jose? Answer by greenestamps(13203) (Show Source):
Jose's age is 7 years more than 3 times Ana's age:
(1)
The product of their ages is 110:
(2)
Substitute (1) into (2):
You can try to factor the quadratic; or you can use the quadratic formula.
Since the factoring requires some trial and error, you might as well skip the formal algebra and solve the problem with mental arithmetic.
What are the pairs of numbers that have a product of 110? Which of those pairs satisfies the condition that one of the numbers is 7 more than 3 times the other?
110 = 110*1
110 = 55*2
110 = 22*5
110 = 11*10
22 = 3(5)+7; so their ages are 5 and 22; and Jose is older.
ANSWER: Jose is 22.
You of course should know how to solve problems like this using formal algebra.
But sometimes those methods don't get you any closer to the solution to a problem than you were at the start. This problem is an example of how sometimes the easiest path to the solution to a problem is mental arithmetic with a little trial and error.
