   SEARCH HOME Math Central Quandaries & Queries  Question from Maria, a parent: Juanita and Jim each think of a number. Juanita's number is 8 more than Jim's number. The product of the two numbers is 65. What is Jim's number? Hi Maria,

Write 65 in terms of its prime factors. 65 = 5 × 13. What I see is that 13 is 8 more than 5 so Jaunita's number is 13 and Jim's number is 5.

I don't think this is how you are expected to solve the problem. I think that you are expected to use algebra so I am going to solve a similar problem using algebra.

Juanita and Jim each think of a number. Juanita's number is 8 more than Jim's number. The product of the two numbers is 308. What is Jim's number?

Let Jim's number be a then Jaunita's number is 8 more than Jim's so Jaunita's number is a + 8. The product of the two numbers is 308 so

a(a + 8) = 308

or

a2 + 8a - 308 = 0.

Factoring this I get

(a - 14)(a + 22) = 0

so a = 14 or -22. I expect they both thought of positive numbers so Jim's number is 14 and Jaunita's number is 14 + 8 = 22.

(Check that 14 × 22 = 308.)

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.