Question

Wilson is 6 years older than Mary. Wilson's age is 10 years less than five times Mary's age. The equations below model the relationship between Wilson's age (w) and Mary's age (m):
w = m + 6
w = 5m − 10

Which is a possible correct method to find Wilson's and Mary's ages?

Answer 1

Wilson is 6 older than mary
w=6+m

wilson is 10 less than 5 times mary
w=-10+5m
w=5m-10


so now we set them eqal to each other since both equal w

m+6=w=5m-10
m+6=5m-10
minus m both sides
6=4m-10
add 10 to both sides
16=4m
divide both sides by 4
4=m
sub back
w=m+6
w=4+6
w=10

wilson=10
mary=4

the correct method is math

Answer 2

You can use substitution to find the solution.
Lets start by solving for m in the first equation.
w - 6 = m + 6 - 6 this leaves it as an equation of m
Now we can put this in place of m in the second equation.
w = 5(w - 6) - 10
w = 5w - 30 - 10
w = 5w - 40
w - 5w = -40
-4w = -40
-4w/-4 = -40/-4
w = 10
So now you put 10 in place of w.
10 - 6 = m + 6 - 6
4 = m
Mary is 4 and Wilson is 10
Put these in place of m and w in the other equation as well to double check.
10 + 10 = 5(4) - 10 + 10
20 = 20 
So this is correct