7. A person has $10,100 to invest in two different stock. Stock ABC costs $32 per share and pays dividends of $1.20 per share. Stock XYZ costs $23 per share and pays dividends of $1.40 per share. If she wants to earn a total of $540 in dividends, how much money should be invested in company ABC?

invested in ABC = $3200

Step-by-step explanation:

given data

total invest = $10,100

Stock ABC costs = $32 per share

dividends = $1.20 per share

Stock XYZ costs = $23 per share

dividends = $1.40 per share

earn a total dividends = $540

solution

we can say total money invest express as

total money invested = 32 * P + 23 * Q

here person buys stocks of ABC is P and buys stocks of stocks of XYZ is Q

$10,100 = 32 * P + 23 * Q

we can also write this as by multiply 3 both side

$30,300 = 96 * P + 69 * Q ... 1

and total dividends will be

total dividends = 1.2 * P + 1.4 * Q

$540 = 1.2 * P + 1.4 * Q

we can also write this as by multiply 80 both side

$43200 = 96 * P + 112 * Q ... 2

so from equation 1 and 2, subtracting 1 from 2

we get

Q = 300

and P = 100

so that we invest 100 * 32

invested in ABC = $3200