Jacqueline was one-third as young as her grandmother 15 years ago. If the sum of their ages is 110, how old is Jacqueline's grandmother?
15 yrs ago:
Jac --- x
grandma -- 3x
now
Jac --- x+15
grandma -- 3x + 15
x+15 + 3x+15 = 110
solve for x, then sub into 30+15
75
To solve this problem, let's begin by defining some variables. Let's assume Jacqueline's current age is J, and her grandmother's current age is G.
We are given that 15 years ago, Jacqueline was one-third as young as her grandmother. This means that Jacqueline's age 15 years ago was J - 15, and her grandmother's age 15 years ago was G - 15.
According to the problem, Jacqueline was one-third as young as her grandmother 15 years ago. So we can set up the equation:
J - 15 = (1/3)(G - 15)
Next, we are given that the sum of their ages is 110. So we can set up another equation:
J + G = 110
Now we have a system of two linear equations:
J - 15 = (1/3)(G - 15)
J + G = 110
To solve this system, we can use substitution or elimination. Let's use substitution:
From the second equation, we can isolate J:
J = 110 - G
Now substitute this value of J into the first equation:
110 - G - 15 = (1/3)(G - 15)
Simplify the equation:
95 - G = (1/3)(G - 15)
Multiply both sides by 3 to get rid of the fraction:
3(95 - G) = G - 15
285 - 3G = G - 15
Combine like terms:
285 = 4G - 15
Add 15 to both sides:
300 = 4G
Divide both sides by 4:
G = 75
So Jacqueline's grandmother is 75 years old.