SOLUTION: The average age of the Johnsons' cars is 8 years. Three years ago the Toyota was twice as old as the Ford. Two years ago the sum of the Buick's and the Ford's ages was equal to the
Question 62307: The average age of the Johnsons' cars is 8 years. Three years ago the Toyota was twice as old as the Ford. Two years ago the sum of the Buick's and the Ford's ages was equal to the age of the Toyota. How old is each car now?
Where do I start? Any help is appreciated.
Found 2 solutions by uma, ankor@dixie-net.com:Answer by uma(370) (Show Source):
You can put this solution on YOUR website! Let the age of Ford be x yrs.
So Ford's age 3 years ago = x - 3
The Toyota's age = 2(x-3)
Age of toyota 2 yrs ago = 2(x-3)+1
Age of Ford 2 yrs ago = x-2
Thus age of BUick 2 yrs ago = 2(x-3)+ 1-(x-2)
= 2x - 6 + 1 - x + 2
= x - 3
Present age of Ford = x
Present age of Toyota = 2x - 3 [because 2(x-3)+1 +2]
Present age of Buick = x - 1 [because x - 3 + 2]
sum of the ages of these cars = x + 2x - 3 + x - 1
= 4x - 4
Average of these cars = (4x - 4)/3
==> (4x-4)/3 = 8
==> 4x - 4 = 24 [multiplying by 3 on either side]
==> 4x - 4 + 4 = 24 + 4
==> 4x = 28
==> 4x/4 = 28/4
==> x = 7
That is the age of Ford = 7 yrs
Age of Toyota = 2x - 3
= 2*7 - 3
= 14 - 3
= 11 yrs
Age of Buick = x - 1
= 7 - 1
= 6 yrs
You can put this solution on YOUR website! Start by writing an equation for each statement, simplify each equation as much as you can: Let the ages of the 3 cars now be: T, F, B
:
"The average age of the Johnsons' cars is 8 years."
(T + F + B)/3 = 8
Get rid of the denominator, mult eq by 3
T + F + B = 24
:
"Three years ago the Toyota was twice as old as the Ford."
T - 3 = 2(F-3)
T - 3 - 2F - 6
T = 2F - 6 + 3
T = 2F - 3
:
"Two years ago the sum of the Buick's and the Ford's ages was equal to the age of the Toyota."
(B-2) + (F-2) = (T-2)
B + F - 4 = T - 2 + 4
B + F = T+2
:
Look at the first equation: T + (F + B) = 24
We just learned that F+B = T+2
:
Replace (F+B) with (T+2) in the 1st equation and we have:
T + (T+2) = 24
2T = 24- 2
2T = 22
T = ll yrs old is the Toyota now
:
Use the equation T = 2F - 3, to find F:
2F - 3 = 11
2F = 11 + 3
F = 14/2
F = 7 yrs old is the Ford
An easy task to find the age of the Buick:
T + F + B = 24
11 + 7 + B = 24
B = 24-18
B = 6 yrs old is the Buick
:
Check our solutions in (B-2) + (F-2) = (T-2)
4 + 5 = 9
:
:
It is often daunting to look at the big picture in these problems. Usually each statememt can be translated to a simple equation. After you have done this a logical method of substitution will emerge.
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