Word Problem Equation

Question

The ages of Jon and Sam total 27 years. In 4 yeas Sam's age plus twice Jon's age will be 43. What are Jon and Sam's ages?

Answer 1

This is in reference to the answer below by Sam.  His process is great, but that second sentence can be tricky.  Usually the "in 4 years" part applies to both of their ages.  Which would make the second equation

 

2(x+4) + (y+4) = 43

 

Then,

2x + 8 + y + 4 = 43

2x + y = 31

 

The first equation remains x + y = 27

 

Subtracting the equations, we get that x = 4.

 

So Jon is currently 4 and Sam is currently 23.

In 4 years Jon will be 8 and Sam will be 27.  Adding twice Jon's age and Sam's age (in four years) would be 16 + 27 = 43.

Answer 2

Let x be defined as Jon's age and let y be defined as Sam's age. So, we know that

 

x+y=27

 

Also, we know that      2x+y+4=43 (twice Jon's age plus Sam's age plus the "in 4 years" part)

 

Subtracting 4 from both sides of the second equation gives us 2 equations:

 

 x+y=27

2x+y=39

 

Subtracting equation 2 from equation 1 yields

 

-x=-12     meaning x=12

 

Plugging that result into equation 1 gives us y=15

 

So Jon's age is 12 and Sam's age is 15