If you add​ Natalie's age and​ Fred's age, the result is 46. If you add​ Fred's age to 4 times​ Natalie's age, the result is 91. Write and solve a system of equations to find how old Fred and Natalie are.

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.