Vern sold his 1964 Ford Mustang for $55,000 and wants to invest the money to earn him 6.4% interest per year. He will put some of the money into Fund A that earns 4% per year and the rest in Fund B that earns 10% per year. How much should he invest into each fund (in dollars) if he wants to earn 6.4% interest per year on the total amount?

Fund A:
Fund B:

Fund A = $33000

Fund B = $22000

Step-by-step explanation:

Let x represent the amount which he should invest in fund A.

Let y represent the amount which he should invest in fund B.

Vern sold his 1964 Ford Mustang for $55,000 and wants to invest the money to earn him 6.4% interest per year. He will put some of the money into Fund A that earns 4% per year and the rest in Fund B that earns 10% per year. This means that

x + y = 55000

The formula for determining simple interest is expressed as

I = PRT/100

Considering fund A,

P = $x

T = 1 year

R = 4℅

I = (x × 4 × 1)/100 = 0.04x

Considering fund B,

P = $y

T = 1 year

R = 10℅

I = (y × 10 × 1)/100 = 0.1y

The interest on the total amount is

0.064(x + y)

If he earns $216.00 in interest in one year from both accounts combined, it means that

0.04x + 0.1y = 0.064(x + y) - - - - - - -1

Substituting x = 55000 - y into equation 1, it becomes

0.04(55000 - y) + 0.1y = 0.064(55000 - y + y)

2200 - 0.04y + 0.1y = 3520

- 0.04y + 0.1y = 3520 - 2200

0.06y = 1320

y = 1320/0.06

y = 22000

x = 55000 - 22000

x = $33000

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: