word problem

[tnelson0504]

Can someone help me? I don't know where to start. Omar is 3 times as old as Jason. Henry is 5 years older than Jason. If their total age is 80 years old, how much older is Omar than Henry?

 

[Deleted member 4993]

Can someone help me? I don't know where to start. Omar is 3 times as old as Jason. Henry is 5 years older than Jason. If their total age is 80 years old, how much older is Omar than Henry?

Let's define variables first. Let

Omar's age = M

Jason's age = J

Henry's age = H

Need to find

M - H = ?

Given:

M = 3*J

H = J + 5

M + J + H = 80

Now continue.....

 

[Mrspi]

Can someone help me? I don't know where to start. Omar is 3 times as old as Jason. Henry is 5 years older than Jason. If their total age is 80 years old, how much older is Omar than Henry?

You've already seen one response. Here's a slightly different way to approach the problem.

We STILL need to define variables, but since I notice that both Omar's and Henry's ages are given in terms of Jason's age, we could do this:

let j = Jason's age
then 3j = Omar's age
and j + 5 = Henry's age

We are told that the total of their ages is 80 years.

Jason's age + Omar's age + Henry's age = 80
j + 3j + (j + 5) = 80

Now...can you solve that for j? Once you know j (which is Jason's age), you can find Omar's age and Henry's age easily. And it should also be easy to determine how much older Omar is than Henry.

 

[BigGlenntheHeavy]

$\displaystyle Another \ way, \ rref \ (reduced \ row \ echelon \ form), \ to \ wit:$

$\displaystyle \ Omar \ \ \ \ Jason \ \ \ \ Henry$

$\displaystyle \ \ 1 \ \ \ \ \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ 80$

$\displaystyle \ \ 1 \ \ \ \ \ \ \ \ \ \ -3 \ \ \ \ \ \ \ \ \ \ \ 0 \ \ \ \ \ \ \ \ 0$

$\displaystyle \ \ 0 \ \ \ \ \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ \ \ \ -1 \ \ \ \ -5$

$\displaystyle Hence, \ Omar \ = \ 45, \ Jason \ = \ 15, \ and \ Henry \ = \ 20.$