The Jones family has two dogs whose ages add up to 15 and multiply to 56. How old is each dog?

Question

I really and struggling with guess and check in math. I need help

Answer 1

Hi Morgan

Kemal has an algebraic solution. You talk about guess and check. If that is the way you are supposed to do the problem here are other solutions.

the ages add up to 15 and multiply to make 56

one solution...

1+14 no

2+13 no

3+12 no

4+11 no

5+10 no

6+9 no

7+8 yes because 8*7=56

another solution...

56=2*2*2*7=(2*2*2)*(7)=8*7 and 8+7=15

Answer 2

Hi Morgan,

 

Let the dogs' ages be x and y. Then, we can write

x + y = 15, and

xy = 56

 

express x in terms of y to reduce the number of variables to one.

x + y = 15

x = 15 - y

Replace x by the above in xy = 56

(15 - y)y = 56

15y - y^2 = 56

Move the terms on the left to the right and write in polynomial form.

y^2 - 15y + 56 = 0

Factorize

(y - 8)(y - 7) = 0

y = 7 or y =8

when y = 7, x = 8

when y = 8, x = 7.