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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?
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1 Answer

(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)
 
Don't forget to put the units with your answers.
 
 
 
 
 

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