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If you add​ Natalie's age and​ Fred's age, the result is 36. If you add​ Fred's age to 4 times​ Natalie's age, the result is 72. Write and solve a system of equations to find how old Fred and Natalie are.

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linandrew41

The known facts

  • the sum of Natalie's age and Fred's age is 36
  • the sum of Fred's age times four and Natalie's age is 72

Now, let's set up the equations where N is Natalie's age and F is Fred's age.

N + F = 36   ---- equation 1

N + 4F = 72 ---- equation 2

equation 2 minus equation 1 ---> 3F = 36 ---> F = 12, thus N = 24

Thus Fred is 12 years old, and Natalie is 24 years old.

Answer:

in this problem, we are going to translate our words into a mathematical equation, solve the equation and then answer the question. So we have, the father is three years older than the mother, so is three, is our answer there for this equation. So if we take the oldest minus the youngest, It would give us a difference of three. So since the father is older, we're going to say the father's age minus the mother's age is three, So we know that the mother is 42 years old, So the father minus the 42 would give us three. So to solve for F, we're going to use the addition property of equality and add 42 to both sides. So F -40 to plus 42 is F and Add 42 to both sides, and three plus 42 is 45. So this means that the father is 45 years old.

Step-by-step explanation:

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