SOLUTION: Henry has two less than one-third as many matchbox cars as Jonah. Micah has four more than twice as many matchbox cars as Jonah. If the three boys have 82 matchbox cars, how many c

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Henry has two less than one-third as many matchbox cars as Jonah. Micah has four more than twice as many matchbox cars as Jonah. If the three boys have 82 matchbox cars, how many c      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1188835: Henry has two less than one-third as many matchbox cars as Jonah. Micah has four more than twice as many matchbox cars as Jonah. If the three boys have 82 matchbox cars, how many cars does Jonah have?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Assign a variable to the number of matchbox cars that Jonah has, follow the description literally and form the described expressions and equation. Solve! 

Henry           (j/3)-2
Jonah            j
Micah            2j+4
SUM              82

j%2F3-2%2Bj%2B2j%2B4=82

j%2F3%2B3j%2B2=82
j%2F3%2B3j=80
j%2B9j=240
10j=240
highlight%28highlight%28j=24%29%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The solution from the other tutor is fine.

Personally, I would set up the problem a bit differently to make solving the problem easier.

Since the number Henry has is 2 less than one-third the number Jonah has, I would start by using 3x instead of x as the number Jonah has. That will allow me to set up an equation without fractions, which is always a little easier. So

3x = # Jonah has
x-2 = # Henry has (2 less than one-third of Jonah's)
6x+4 = number Micah has (4 more than twice Jonah's)

Now write and solve the equation that says the total number is 82:

(3x)+(x-2)+(6x+4)=82
10x+2=82
10x=80
x=8

ANSWER: The number Jonah has is 3x = 24

CHECK:
Henry: x-2 = 6
Micah: 6x+4 = 52
24+6+52 = 82 correct!