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KATRIN_1 [288]
3 years ago
6

A total of $12,000 is invested in two corporate bonds that pay 7.5% and 9% simple interest. The invest wants an annual interest

income of $990 from investments. What amount should be invested in the 7.5% bond?
Mathematics
1 answer:
nlexa [21]3 years ago
6 0

Answer:

$13,200

Step-by-step explanation:

You need to use the simple interest formula

I = P * r * t

I = Interest accrued

P = Principal amount invested

r = Interest rate          you need to divide by 100 to get it in decimal form

t = time, in years        if you are given a partial year, divide the months by 12

P = $12,000                                    

r = 7.5% = .075                                    

t = 1                                                  

But, because we want I to equal $990 then I is

I = $990

So we ignore our P and instead solve for the P that will give us the desired result.

I = P * r * t

$990 = P * .075 * 1

$990 = P.075        Divide each side by .075

$990/.075 = P.075/.075

$990/.075 = P

$13,200 = P

So, to earn an annual interest income of $990, $13,200 will have to be invested in the 7.5% bond.

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Anna [14]

Answer:

The florist can make 11 regular bouquets and 21 mini bouquets

Step-by-step explanation:

The number of roses the florist has = 118 roses

The number of peonies the florist has = 226 peonies

The number of roses in each regular bouquet = 5 roses

The number of peonies in each regular bouquet = 11 peonies

The number of roses in each mini bouquet = 3 roses

The number of peonies in each mini bouquet = 5 peonies

1. The equation that gives the total number of roses to be used in both kinds of bouquet is given as follows;

Let r represent the number of regular bouquet the florist can make and let m represent the number of mini bouquet the florist can make, we have;

5·r + 3·m = 118...(1)

2. Similarly, we have;

11·r + 5·m  = 226...(2)

Making m the subject of the formula of both equations, and equating both values of m to find a common solution, we have;

m = (118 - 5·r)/3

m = (226 - 11·r)/5

(118 - 5·r)/3 = (226 - 11·r)/5

5 × (118 - 5·r) = 3 × (226 - 11·r)

590 - 25·r = 678 - 33·r

33·r - 25·r = 678 - 590 = 88

8·r = 88

r = 88/8 = 11

r = 11

The number of regular bouquet the florist can make = r = 11

m = (118 - 5·r)/3 = (118 - 5×11)/3 = 21

m = 21

The number of mini bouquet the florist can make = m = 21

The number of regular bouquet the florist can make = 11 bouquets

The number of mini bouquet the florist can make = 21 bouquets.

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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