Answer:
Fred = 31
Natalie = 15
Step-by-step explanation:
We have Natalie and Fred's whos age are unknown, we know that when added, their ages equal 46. While when multiplied with Natalie's age 4 times, their ages is 91.
Create two systems :
F = Fred
N = Natalie
F + N = 46
4N + F = 91
We can change the first equation to Natalie's age alone :
N = 46 - F
Now substitute this into the second equation :
4(46 - F) + F = 91
Distribute :
184 - 4F + F = 91
Subtract 184 from both sides :
-4F + F = -93
Add like terms :
-3F = -93
Divide -3 from both sides :
F = 31
Therefore, Fred is 31 years old. Now replace his age in the first equation :
31 + N = 46
46 - 31
15
Therefore, Natalie is 15 years old.
