SOLUTION: Jason's age is 3 times Shauna's present age.In 4 years' time, the sum of their ages will be 56 years. Find their present age

Question 1153652: Jason's age is 3 times Shauna's present age.In 4 years' time, the sum of their ages will be 56 years. Find their present age
Found 3 solutions by MathLover1, ikleyn, MathTherapy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

let Jason's age be and Shauna's age
if Jason's age is times Shauna's present age, we have
....eq.1
if in years' time, the of their ages will be years, we have

.......substitute from eq.1

go to eq.1
....eq.1,substitute

their present age: Jason's is and Shauna's is

Answer by ikleyn(52792)   (Show Source): You can put this solution on YOUR website!
.

            It can be solved in much simpler way.
            You do not need to use the system of two equations.
            One equation is totally enough.

Let x be the Shauna's age; then the Jason's age is 3x years. In 4 years time, the Shauna's age will be (x+4) years, while the Jason's age will be (3x+4) years. The condition says (x+4) + (3x+4) = 56 years. It is your basic equation. Simplify it and solve for x 4x + 8 = 56 4x = 56 - 8 = 48 4x = 48 x = = 12. ANSWER. Shauna is 12 years old; Jason is 3*12 = 36 years old.

            You even may to solve the problem MENTALLY.

In 4 years, the sum of their ages will be 56 ---- hence, the sum of their ages now is 56-4-4 = 48 years. At the same time, Jason's age is 3 times Shauna's age --- hence, they are 12 and 36 years, and this simple calculation you can do in your mind (!), obtaining the SAME ANSWER.

Surely, both solutions use the same logic.

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There is a bunch of lessons on age word problems
    - Age problems and their solutions
    - A fresh formulation of a traditional age problem
    - Really intricate age word problems
    - Selected age word problems from the archive
    - Age problems for mental solution
    - Miscellaneous age problems
in this site.

Read them and become an expert in solving age problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Age word problems".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

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Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Jason's age is 3 times Shauna's present age.In 4 years' time, the sum of their ages will be 56 years. Find their present age

Let Shauna's age be S
Then Jason's is: 3S
We then get: S + 3S + 2(4) = 56
4S = 48
S, or Shauna is:
It's now simple as 1-2-3 to find Jason's age!
Using 1 variable is most often much easier and less confusing than using 2!!
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