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# Applications of system of equation

(1)Maria invested \$5500 in two mutual funds.One fund earned an 8% profit,while the other earned a 1.5% profit.Between the two accounts,Maria made a profit of \$180. How much was invested in each account?

(2) Raheem can buy peanuts for \$0.40 per pound and cashews for \$1.05 per pound.How many pounds of each type should he buy to produce 120 pounds of a mixture that costs him \$0.66 per pound?

### 1 Answer by Expert Tutors

Felice R. | Need Help in Math and Science - Engineer willing to helpNeed Help in Math and Science - Engineer...
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(1)The best thing to do with word problems is list all the info you have and need assigning variables

it = total money invested = 5500

if1 = amount invested in fund 1
if2 = amount invested in fund 2 = it - if1 = 5500 - if1

pf1 = profit fund 1 = 8% = .08            (a percent to decimal    you need to divide percent number by 100)
pf2 = profit fund 2 = 1.5% = 0.015
p = profit = 180 = pf1*if1 + pf2*if2

since I have set up the amount invested in fund 2 as a function of amount invested in fund 1 lets solve for if1 using the profit equation

p = pf1*if1 + pf2*if2
180 = .08 * if1 + .015*if2      (substitute in known values)
180 = .08*if1 + 0.015 *(5500-if1)   (substitute in eqn using if1 for if2)

now solve for if1

180 = 0.08 * if1 + 82.5 - 0.015*if1
180- 82.5 = (0.08-0.015) * if1
if1 = 97.5/0.065 = 1500

which would mean
if2 = 5500 - if1 = 5500 - 1500 = 4000

Now lets verify that the answer is correct using the profit eqn again

p = 0.08*1500 + 0.015 * 4000
p = 120 + 60
p = 180   We get the same answer so values are correct

Full Answer is \$1500 invested into fund 1 and \$4000 invested into fund 2   (don't forget the units)

(2) Now I will help set up the second problem but you will need to solve for it

C= cost of peanuts = \$0.40/lb
CC = cost of cashews = \$1.05/lb

PN = total pounds of nut mixture = 120 lb
PP = pounds of peanuts
PC = pounds of cashews = PN - PP = 120 - PP

CN = cost of nut mixture = \$0.66/lb

CN*PN = 120lb * \$0.66/lb = \$79.20 = CP*PP + CC*P     (this is total money spent on all nuts)

Good luck, you need to solve for PP and then PC.
Verify your answer using the total money spent on all nuts (\$79.20)