SOLUTION: Mark won a lottery and received $74,000; he invested part of it in his retirement account and donated the rest to a charity. The amount of the donation was $500 less than a quarte

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Question 1139492: Mark won a lottery and received $74,000; he invested part of it in his retirement account and donated the rest to a charity. The amount of the donation was $500 less than a quarter of the amount of the investment. How much did Mark invest in his retirement account and how much did he donate to the charity?
(a) Define your variable(s).
(b) Construct a mathematical model (equation) in one unknown.
(c) Solve the equation constructed.
(d) Write a sentence to represent your findings
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
mark wins the lottery and receives 74,00.
he invest part of it and donates the rest to charity.
the amount he donates is 500 less than a quarter of the amount of the investment.
how much did he invest in his retirement account and how much did he donate to charity.

let x equal the amount he donated to charity.
74,000 is the amount he received.
the amount he donated is 500 less than one quarter of the amount of the investment.

if we let x equal the amount he donaterd to charity and if we let y equal the amount he invested, we get:

x + y = 74,000
x = 1/4 * y - 500

replace x with 1/4 * y - 500 in the equation of x + y = 74,000 to get:

1/4 * y - 500 + y = 74,000

add 500 to both sides of this equation to get 1/4 * y + y = 74,500.

combine like terms to get 5/4 * y = 74,500

solve for y to get y = 74,500 * 4/5 = 59,600.

since x + y = 74,000, then x must be equal to 74,000 - 59,600 = 14,400.

it appears that your solution is that he invested 59,600 in his retirement account and he donated 14,400 to charity.

all we need to do is to confirm that this is correct.

x + y = 74,000 becomes 14,400 + 59,600 = 74,000 which is true.

x = 1/4 * y - 500 becomes x = 1/4 * 59,600 - 500 which becomes x = 14,400 which is true.

the solution looks good.

the solution is that he invested 59,600 in his retirement account and donates 14,400 to charity.









Answer by MathTherapy(10557)   (Show Source): You can put this solution on YOUR website!
Mark won a lottery and received $74,000; he invested part of it in his retirement account and donated the rest to a charity. The amount of the donation was $500 less than a quarter of the amount of the investment. How much did Mark invest in his retirement account and how much did he donate to the charity?
(a) Define your variable(s).
(b) Construct a mathematical model (equation) in one unknown.
(c) Solve the equation constructed.
(d) Write a sentence to represent your findings
Getting you started by doing a) and b)

Let amount donated to charity be C 

Then amount invested in retirement account = 74,000 - C

The CORRECT equation in ONE UNKNOWN, or in ONE VARIABLE, as requested, is: 

Now, solve that for C, the amount donated, after which C should be subtracted from 74,000 to get amount invested. 

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