Having trouble with math problem

Factual Questions
1

Hello Dopers!I am trying to solve this problem but I cant. I have thought about it for some days and I still cant figure it out. Any help would be appreciated!

Bob, Maria, and Shoshana all have birthdays on the same day. Bob’s present age is two years less than the sum of Shoshana’s and Maria’s present ages. In five years, Bob will be twice as old as Maria will be then. Two years ago, Maria was half as old as Shoshana was. How old is each of them?

I tried setting up linear equations but I am not sure if they are correct:
b-2=s+m
b-2+5=m / 2
M-2=s / 2
Any help would be apperciated. Thanks

2

I am probably going to embarass myself by making some silly mistake here, but I will give it a go.

Bob’s present age is two years less than the sum of Shoshana’s and Maria’s present ages. This means add Shoshana’s age with Maria’s age and subtract two to get Bob’s age.

b = s + m - 2

In five years, Bob will be twice as old as Maria will be then. That means we can get the same number by either adding 5 to Bob’s age or adding 5 to Maria’s age and doubling it.

b + 5 = 2(m + 5)

Two years age Maria was half as old as Shoshana was. So if we subtract two years from both of them, we need to divide Shoshana’s result in half to get Maria’s.

m - 2 = (s - 2)/2

3

I agree with MG’s equation set-up.

I take it you know where to go after that.

4

What you have at the core of it is a language problem, accurately translating from “English” to “Math.” You’re not alone, word problems have been the bane of many a math student for ages.

Let’s look at the first part–Bob’s present age is two years less than the sum of Shoshana’s and Maria’s present ages. For this you have b-2=s+m. It’s backwards. Bob’s present age is already 2 less than s+m, and you’re taking 2 more off of it. In order for b, which is 2 less than s+m, to become to equal s+m, you’ve got to add 2 to it. This would be b+2=s+m, which is essentially the same as MentalGuy’s b=s+m-2.

My wording could be criticized in that b itself does not actually become equal to s+m, it remains b. It’s changing b into b+2 that gives you a value equal to s+m. What I’m trying to do is give you examples of other ways to express the problem in English. Sometimes that gives insight into how to express the problem in algebra.

5

Bob, Maria, and Shoshana all have birthdays on the same day.

Bob’s present age is two years less than the sum of Shoshana’s and Maria’s present ages.

Take b, m and s as the current ages. therefore :

b = (m + s) - 2

In five years, Bob will be twice as old as Maria will be then.

in five years, bob’s age b will become (b + 5). maria’s age in five years will also become (m + 5). this new age of bob will be twice as old as this new age of maria.

so,

b + 5 = 2(m+5)

Two years ago, Maria was half as old as Shoshana was.

Two years ago, Maria was (m-2) and Shahana was (s-2).
maria’s this age was half of shoshana’s this age.

so,

m-2 = 1/2(s-2)
so the equations are :

b = (m + s) - 2

b + 5 = 2(m+5)

m-2 = 1/2(s-2)

Solving for them, you get current ages as:

Bob = 23
Maria = 9
Shoshana = 16

Putting these answers back into the question, we get:

Bob, Maria, and Shoshana all have birthdays on the same day. Bob’s present age (23) is two years less than the sum (25) of Shoshana’s (16) and Maria’s (16) present ages. In five years, Bob (28) will be twice as old as Maria (14) will be then. Two years ago, Maria (7) was half as old as Shoshana (14) was. How old is each of them? 23, 9 and 16.

So MentalGuy’s equations were correct but maybe this explanation might make it easier for you to understand why.

6

Thanks alot MentalGuy and xash. I apperciate the help