If Kurt were 10 years old, he would be twise as old as his sister, and their combine ages would be 36. How old are Kurt and his sister?
Did you mean "If Kurt was 10 years older" ?
The way you have it, Kurt is 10, his sister would have to be 5, but then their combined ages can't be 36
If as I think it should be,
let Kurt's present age be x
let his sister's present age by y
in 10 years ...
Kurt = x+10
sister = y +10
we are told that Kurt is twice her age at that time ...
x+10 = 2(y+10)
x = 2y + 10
also x+10 + y+10 = 36
x + y = 16
sub in x = 2y+10
2y+10 + y = 16
3y = 6
y = 2 , then x = 14
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To determine the ages of Kurt and his sister, let's assign variables to represent their ages. Let's say Kurt's age is "K" and his sister's age is "S".
From the given information, we have two conditions:
1. "If Kurt were 10 years old, he would be twice as old as his sister":
This means if we subtract 10 from Kurt's current age (K - 10), it would be twice his sister's current age (2S).
2. "Their combined ages would be 36":
The sum of Kurt's age and his sister's age should be equal to 36 (K + S = 36).
Now we have a system of two equations with two variables:
(K - 10) = 2S -- Equation 1
K + S = 36 -- Equation 2
We can solve this system to find the values of K and S.
First, let's rearrange Equation 1 to express K in terms of S:
K = 2S + 10 -- Rewritten Equation 1
Substitute this expression for K in Equation 2:
(2S + 10) + S = 36
Combine like terms:
3S + 10 = 36
Subtract 10 from both sides:
3S = 26
Divide both sides by 3:
S = 26 / 3
Simplifying further, we get:
S ≈ 8.67
Now substitute this value of S back into Equation 2 to find K:
K + 8.67 ≈ 36
K ≈ 36 - 8.67
K ≈ 27.33
Since age cannot be in fractions, we can round these values.
Kurt is approximately 27 years old, and his sister is approximately 9 years old.