Alice is three times as old as Jack. In 10 years she will be twice as old as Jack. How old are Alice and Jack now? How old will they be in10 years
A = 3J
A + 10 = 2(J + 10)
Substitute 3J for A in second equation and solve for J. Insert that value into the first equation and solve for A. Check by inserting both values into the second equation.
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Jack=10 years old and Alice 30 years old
To find out how old Alice and Jack are now, we can use algebraic equations based on the information provided.
Let's assume that Alice's current age is A, and Jack's current age is J.
We know that Alice is three times as old as Jack, so we can write the equation A = 3J. This equation represents the relationship between their current ages.
In 10 years, Alice will be A + 10 years old, and Jack will be J + 10 years old. We are also told that in 10 years, Alice will be twice as old as Jack. So, we can write the equation A + 10 = 2(J + 10). This equation represents the relationship between their ages in 10 years.
Now, we have two equations:
1) A = 3J
2) A + 10 = 2(J + 10)
To solve these equations simultaneously, we can substitute the value of A from the first equation into the second equation:
3J + 10 = 2(J + 10)
Let's simplify this equation:
3J + 10 = 2J + 20
Subtracting 2J from both sides of the equation, we get:
3J - 2J + 10 = 2J - 2J + 20
J + 10 = 20
Subtracting 10 from both sides of the equation:
J + 10 - 10 = 20 - 10
J = 10
Now that we know Jack's age is 10, we can substitute this value into the first equation to find Alice's age:
A = 3J
A = 3 * 10
A = 30
Therefore, Alice is currently 30 years old, and Jack is currently 10 years old.
To find how old they will be in 10 years, we add 10 years to their current ages:
Alice will be 30 + 10 = 40 years old.
Jack will be 10 + 10 = 20 years old.
So in 10 years, Alice will be 40 years old, and Jack will be 20 years old.