Question

Mary is twice as old as Helen’s age, If 8 is subtracted from Helen’s Age and 4 is added to Mary Age? Mary will be 4 times as old as Helen. What are the ages

Answer 1

Answer:

set mary is x years old, and helen is y years old.

first sentence:x=2y

second one:4(y-8)=x+4

bring x=2y in 4(y-8)=x+4

=>4y-32=2y+4

=>2y=36

=>y=18

=>x=36

mary:36

helen:18

Answer 2

We want to write and solve a system of equations that models given situation. We will see that Helen is 18 years old, and Mary is 36 years old.

Let's define the variables we will be using.

• m = Mary's age.
• h = Helen's age.

We know that "Mary is twice as old as Helen’s age"

Then:

m = 2*h

"If 8 is subtracted from Helen’s Age and 4 is added to Mary Age, Mary will be 4 times as old as Helen."

(m + 4) = 4*(h - 8)

Then the system of equations is:

m = 2*h

(m + 4) = 4*(h - 8)

To solve it, we can replace m by 2*h in the second equation, so we get:

(2h + 4) = 4*(h - 8)

2*h + 4 = 4*h - 32

4 + 32 = 4*h - 2*h

36/2 = h = 18

And we know that:

m = 2*h = 2*18 = 36

So Helen is 18 years old, and Mary is 36 years old.

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