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Question 4735: Write this equation and solve.
One half of a number is 3 more than one-sixth the same number. What is the number?
Solve the problem.
Hellen Weller had a total of $3000 to invest. She invested part of it in an account paying 2% simple interest and the rest at 4%. Her annual interest income was $100. How much did she invest in each account?
thanks
Answer by Abbey(339)   (Show Source):
You can put this solution on YOUR website! Part One:
Let the number = x
Then:
one half the number is x/2
one sixth the number is x/6
so
One half a number is three more than one-sixth the same number
x/2 = 3+ x/6
multiply the equation by 6 to get rid of the denominators
3x = 18 + x
Consolidate like variables by subtracting x from both sides
3x -x = 18 +x -x
2x = 18
Divide both sides by two
x = 9
plugging 9 back into the equation we find it true
9/2 = 3 + 9/6
4 1/2 = 3 + 1 1/2
4 1/2 = 4 1/2
Part TWO
x = amount invested at 2% simple interest
3000-x = amount invested at 4% interest
.02(x) = amount of interest received at 2%
.04(3000-x) = amount of interest received at 4%
Total interest = amount of interest at 2% + amount of interest at 4%
100 = .02(x) + .04(3000-x)
Clear the parentheses:
100 = .02x + 120 - .04x
Subtracting 120 from both sides:
100-120 = .02x +120 - 120 -.04x
Consolidate like terms:
-20 = -.02x
Divide both sides by .02 to isolate the variable
-20/.02 = -.02x/.02
1000 = x
earlier we determined that
x = amount invested at 2% simple interest
3000-x = amount invested at 4% interest
Therefore:
the amount invested at 2% = $1,000
the amount invested at 4% = $2,000
Check it:
.02*1000 = $20.00
.04*2000 = $80.00
$20.00+$80.00 = $100.00
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