Someone please help me write the equation for a math problem?

Question

we're supposed to solve this with 3 equation and it must have 3 variables.This is the question:
Suppose you have saved $3200 and decide to invest your savings in a growth fund, an income fund, and a money market fund, paying 7%, 10% and 5% simple annual interest, respectively. To get the greaterst return, you decide to put twice as money in the growth fund as in the money market fund. How much should you invsst in each fund to get a return of $250at the end of one year?

P.S. put this in a equation please.

Answer 1

let
x = amount in growth fund,
y = amount in income fund,
z = amount in money market fund


x + y + z = $3,200
0.07x + 0.10y + 0.05z = $250
x = 2z

Answer 2

So you invest an amount A in the money market fund earning 5%, 2A in the growth fund earning 7% and the rest (3200 - 3A) in the income fund earning 10%.

So the equation is 2A * 7% + (3200 - 3A) * 10% + A * 5% = 250

(multiply by 100)

14A + 32000 - 30A + 5A = 25000
-11A + 32000 = 25000
11A = 7000
A = 7000 / 11 = 636.36.

So you invest 2A = 1272.72 in the growth fund
(3200 - 3A) = 1290.92 in the income fund
636.36 in the money market fund

Answer 3

ok...

you're going to put x dollars into the Money market fund
twice as much into the growth fund ( 2x)
and the balance in the income fund (3200-3x)

we know the interest earned by each account and that the total interest earned must equal $250

so... Money market earns x multiplied by 5%
growth fund earns 2x multiplied by 7%
income fund earns (3200-3x) multiplied by 10%

and the sum of these three = $250

so let .05x + .14x + .1(3200 - 3x) = 250
.19x +320 - .3x = 250
.11x = 70

therefore x = 636.36

so

Money market fund needs 636.36
Growth fund needs 1272.72 (2x)
Income fund needs 1290.92 (i.e the balance (3200-3x))


x

Answer 4

if you invest 'x' in the market fund then, 'y' in income fund and 'z' in growth fund, you have the eqn:
x + y + z = 3200 --- (1)
but we know that growth fund is twice market fund:
ie. y = 2x ---- (2)
x + 2x + y = 3200 --- (1) updated.

Now you want a retun of 250 at the end on one year.

ie. (5/100)*x + (7/100)*2x + (10/100)*y = 250 ---- (3)

so the two eqns are (upon simplification):
3x + y = 3200 ----- (1)
19x + 10y = 25000 ---- (3)

When you slove it: x = 636.36 and y=1290.92
so, market fund = x = $636.36
growth fund = 2x = $1272.72
income fund = y = $1290.92

Answer 5

Savings = $3200
GF = 7%, IF = 10%, MMF = 5%

2X x 0.07 + X x 0.05 + (3200 - 3X) x 0.1 = $250 where X is amount placed in the Market fund

0.14X + 0.05X + 320-0.3X = $250

0.19X - 0.3X = -$70

-0.11X = -$70

X = 70/0.11 therefore X = $636.36

So You put $636,36 in the Money Market fund
$1272.72 in the Growth Fund
and $1290.92 in the Income Fund

I think!!

You should have put it all in the highest yield account, obviously!

Answer 6

I'm not sure about using three variables and making three equations. That honestly seems much too complicated, unless the second and third equations just define the relationships between the three variables.

Here's what I'd say:
.1 (i) + .05 (m) + .07 (g) = $250
g = 2m
i = 3200 - (g + m)

Expressing the first equation in terms of one variable (thus rendering it solveable), you would have:
.1 (3200 - 3m) + .05m + .07 (2m) = $250
320 -.3m + .05m + .14m =250
70 = .11m
m = $636.36

Thus, you would put $636.36 in the market fund, $1272.72 in the growth fund, and $1290.92 in the income fund.