Question

Jennifer age 18 initially invested $1000 at 8% interest how old would she be when the account is $128,000

Answer 1

2,304 years old

Explanation:

Given: Jennifer age = 18, Invested = $1000 at 8% interest

To find: How old would she be when the account is $128,000?

Wrong solution

Solution: To figure out how old she will be when her account is $128,000, simply find the difference between her current account value by her current age, by dividing. Then multiply the result by the future account value.

Step 1:
`(1000)/(18) = 55.5555555556`

Rounding, that is; 55.56

Step 2: Now, multiply the result by the future account value.

`55.56` ×
`128000 = 7111680`

Correct solution

Solution: To find out how old she will be when her account is $128,000, set up a fraction;

`(1000)/(8) = (12800)/(x)`

Step 1: Divide the numbers

`(1000)/(8) = (128000)/(x) \\\\(500)/(9) = (128000)/(x)`

Step 2: Multiply all terms by the same value to eliminate fraction denominators

`(500)/(9) = (128000)/(x) \\\\x * (500)/(9) = x * (128000)/(x)`

Step 3: Cancel multiplied terms that are in the denominator

`x *(500)/(9) = x * (128000)/(x) \\\\x * (500)/(9) = 128000`

Step 4: Re-order terms so constants are on the left

`x * (500)/(9) = 128000\\\\(500)/(9) x= 128000`

Step 5: Combine multiplied terms into a single fraction

`(500)/(9) x = 128000\\\\(500x)/(9) = 128000`

Step 6: Multiply all terms by the same value to eliminate fraction denominators

`(500x)/(9) = 128000\\\\9 * (500x)/(9) = 9 * 128000`

Step 7: Cancel multiplied terms that are in the denominator

[tex]9 * \frac{500x}{9} = 9 * 128000\\500