Joan is three years younger than Martin. How old will Joan be when she is 4/5 his age?
Let's break down the information given:
1. Joan is three years younger than Martin.
2. We need to determine Joan's age when she is 4/5 Martin's age.
Let's assign a variable to Martin's age to make it easier to solve the problem. Let's say Martin's age is "M".
1. Since Joan is three years younger than Martin, her age can be expressed as M - 3.
2. To determine Joan's age when she is 4/5 Martin's age, we can set up the equation:
(M - 3) = (4/5)M
Now, we can solve the equation for M:
Multiply both sides of the equation by 5 to eliminate the fraction:
5(M - 3) = 4M
Distribute the 5:
5M - 15 = 4M
Subtract 4M from both sides of the equation:
5M - 4M - 15 = 4M - 4M
Simplify:
M - 15 = 0
Add 15 to both sides of the equation:
M - 15 + 15 = 0 + 15
Simplify:
M = 15
Now that we know Martin's age is 15, we can determine Joan's age at that time:
Joan's age = M - 3 = 15 - 3 = 12
Therefore, Joan will be 12 years old when she is 4/5 Martin's age.
To find out how old Joan will be when she is 4/5 Martin's age, we need to determine their current ages.
Let's say Martin's current age is M.
According to the given information, Joan is three years younger than Martin, so her age would be M - 3.
Now, let's set up an equation to represent the relationship between their ages:
Joan's age = 4/5 * Martin's age.
Substituting the values we have:
M - 3 = (4/5)M.
Now we can solve for M to find Martin's current age:
Multiply both sides of the equation by 5 to remove the fraction:
5(M - 3) = 4M.
Expand the equation:
5M - 15 = 4M.
Subtract 4M from both sides:
5M - 4M - 15 = 0.
Simplify:
M - 15 = 0.
Add 15 to both sides:
M = 15.
Now that we know Martin's current age is 15, we can determine Joan's age:
Joan's age = 15 - 3 = 12.
To find out how old Joan will be when she is 4/5 Martin's age, we multiply 12 (Joan's current age) by 4/5:
12 * 4/5 = 9.6.
Therefore, Joan will be 9.6 (or approximately 10) years old when she is 4/5 Martin's age.
Martin is X yrs. old.
Joan is (x-3) yrs. old.
4x/5 = x-3
Multiply both sides by 5:
4x = 5x-15
X = 15
(4/5) * 15 = 12 yrs. = Joan's age.