Question

The ratio of the ages of Mandy and Sandy is 2:5. After 8 years, their ages will be in the ratio 1:2. What is the difference between their present ages?

Caitlin says the difference in their ages is 24 years. In two or more complete sentences, explain whether or not Caitlin is correct. In your explanation, include the equations and calculations necessary to support or contradict Caitlin's answer.

Answer 1

@dude

Answer 2

@Mercury

Answer 3

you'll have to set up a system of equations, one that represents their current ages, and one that represents their future ages

let's let m = the current age of Mandy and s = the current age of Sandy

right now, the ratio of Mandy's age: Sandy's age = 2:5 ---> therefore m/s = 2/5
if we solve this equation for s, we get s = 5m/2

now, in 8 years, their future ages will be m + 8 and s + 8 respectively, and since mandy's future age: sandy's future age = 1:2, then (m+8)/(s+8) = 1/2

now, since we want to solve for one of the ages, plug in s = 5m/2 from the previous step into (m+8)/(s+8) = 1/2, and solve the resulting equation for m.

from there, s = 5m/2 so you can plug in mandy's age to get sandy's age

Answer 4

to address the second part of the question, "Caitlin says the difference in their ages is 24 years." ---> simply subtract (m-s), take the absolute value if the result is negative, then see whether it's equal to 24 or not