Can anyone help answer this math problem?

Question

Tell me if this is easier than it sounds:

Shirley is 21 years older than Laura. In six years, Shirley will be twice as old as Laura. How old are they now?

I feel like Shirley is ALWAYS going to be as twice as old as Laura if she also is in six years. Is this just a trick question? Any help is appreciated.

Answer 1

she will only be twice as old as her once...

you can model this using equations:
S = L + 21 ... (shirley is 21 years older than laura)
S + 6 = 2(L + 6) ... ( in 6 years, shirley will be 2x as old as laura)

substituting S into the second equation:
(L+21) + 6 = 2L + 12
L - 2L = 12 - 21 - 6
-L = -15
Laura is 15 years old

S = L + 21
S = 15 + 21
S = 36
Sharon is 36 years old

Answer 2

let S= Shirley's age
let L = Laura's age

S = L + 21 Shirley is 21 years older than Laura.
S - 21 = L + 21 - 21
S - 21 = L

S + 6 = 2(L + 6) Shirley's age in 6 years will be twice Laura's
age in 6 years.
S + 6 = 2L + 12
S + 6 - 12 = 2L + 12 - 12
S - 6 = 2L
so S - 6 = 2(S - 21)
S - 6 = 2S - 42
S - 6 + 42 = 2S - 42 + 42
S + 36 = 2S
S + 36 - S = 2S - S
36 = S

therefore, S = 36
L = S - 21 = 36 - 21 = 15

so Shirley is 36 years old and Laura is 15.

also, in 6 years, Shirley will be 42 and Laura will be 21, which means in 6 years, Shirley will be twice Laura's age in 6 years.

Answer 3

This is easy. Let me answer this logically in words instead of equations.

Shirley will always be 21 years older than Laura. In six years, when Shirley is twice as old as Laura, she'll be 42 and Laura 21. This is the only possible combination. That means Shirley is 36 now and Laura 15.

See the light? Hope this helps. I know it takes time to figure out all those equations with variables, especially 2 variables.

Answer 4

A is 1 when her brother B is 5 (B is 5 times older)
A is 2 when her brother B is 6 (B is 3 times older)
A is 4 when her brother B is 8 (B is twice as old)

and so on (for the same A and B followed over 3 years).

Here, use S for Shirley's age and L for Laura's age:

First statement says:
S - L = 21

Second statement says "in six years" therefore Shirley's age will be S+6 and Laura's age will be (L+6)
(S+6) = 2*(L+6)

S + 6 = 2*L + 12

S - 2L = 12 - 6 = 6

Solve (you have two unknowns and two equations)

Answer 5

For word problems, we try and recognize who/what everything is being compared to, and assign that our variable.
In this case, the problem says Shirley is 21 years older than Laura, so let's let x = Laura's present age.

It follows that:

x = Laura's present age
x + 21 = Shirley's present age.

Here is where you make a chart:

AGE NOW:
Laura: x, Shirley: x + 21

AGE IN 6 YEARS:
Laura: x + 6. Shirley: x + 21 + 6, or x + 27

We know that in 6 years, Shirley will be twice as old as Laura, so
Shirley (who, in 6 years, is x + 27) will be twice as old as Laura (who is, in 6 years, x + 6.

Shirley is twice as old as Laura means
2(x + 6) = x + 27

Now, we solve this algebraic equation.

2x + 12 = x + 27
x = 15

Therefore, Laura is 15 years old. Note that now that we know Laura's age, we can get Shirley's age (x + 21). So Shirley is
15 + 21 = 36 years old.

Laura's age: 15
Shirley's age: 36

Note that in 6 years, Laura will be 21. amd Shirley will be 42. Shirley will be precisely twice Laura's age.

Answer 6

It is.

Let S = Sirley's age
Let L = Laura's age
Then S= L + 21 <-- Eq 1
S +6 = Shirleys age 6 years from now
L + 6 = Laura's age 6 years from now
So S+6 = 2(L+6) <-- Eq 2
Replace S in Eq 2 with L+21 from Eq 1, getting
L+21+6 = 2(L +6) = 2L + 12
L+27 = 2L+12
2L-L = 27 -12
L = 15
S=L+21 = 15+ 21 = 36
So S is 36 and L is 15
6 years from now S=36+6 =42 and L=15+6 =21
So 42 = 2 times 21.

Answer 7

S = age of Shirley now
L = age of Laura now

We have

S = L + 21
S + 6 = 2(L + 6) = 2L + 12
S = 2L + 6

Set the two equations for S equal.

S = L + 21 = 2L + 6
15 = L

S = L + 21 = 15 + 21 = 36

So Laura is 15 and Shirley is 36.

Answer 8

Shirley is 36 and Laura is 15:

Answer 9

LET AGE OF LAURA=X
THEN AGE OFSHIRLEY=X+21
AFTER 6 YRS.

AGE OF LAURA WILL BE=X+6
AND AGE OF SHIRLEY WILL BE=X+27

SO X+27=2(X+6)

X=2X+12-27
15=X
SO AGE OF LAURA IS 15 YRS.
AND AGE OF SHIRLEY IS 36

Answer 10

laura is 15
shirley is 36

in six years:laura ~ 21, shirley ~ 42
in seven years: laura ~ 22, shirley ~ 43

see..... she wont always be twice as old