SOLUTION: Mary's father is four times as old as Mary. Five years ago he was seven times as old. How old is each now? Use the five step method to solve using algebra only.

Question 249488: Mary's father is four times as old as Mary. Five years ago he was seven times as old. How old is each now? Use the five step method to solve using algebra only.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Step 1. Use some letter to represent the unknown quantity.
Step 2. Translate the English into mathematics and create an equation.
Step 3. Solve this equation.
Step 4. Check your work by substituting your results back into the original problem statement.
Step 5. Write your conclusion being sure answer the question asked.
.
STEP 1.
F = Father's age
M = Mary's age
.
STEP 2.
Father is 4 times as old as Mary: F = 4*M, where F=Father's age, and M=Mary's age.
Five years ago F was 7 times older than M.
F-5 = 7(M-5)
F-5 = 7M - 35
.
STEP 3.
substituting F = 4M
4M - 5 = 7M - 35
.
adding 5 to both sides
4M = 7M - 30
.
subtracting 7M from both sides
-3M = -30
.
dividing both sides by -3
M = 10
.
STEP 4.
Mary is 10 now.
Father is 4*10 = 40 now.
.
Five years ago:
Mary was 5.
Father was 35.
Was Father 7 times as old as Mary then?
Yes.
.
Checks.
STEP 5.
Mary is 10 years old now.
Father is 40 years old now.
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