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.

water molecules will move from the side of higher water concentration to the side of lower concentration until both solutions are isotonic. at this point, equilibrium is reached. in an isotonic solution, the flow of water in and out of the cell is happening at the same rate.

hope this < 3

1

step-by-step explanation:

it's the only multiple of both and the least