Formulate the situation as a system of two linear equations in two variables. Be

Question

Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by the elimination method. Be sure to state your final answer in terms of the original question. A lawyer has found 60 investors for a limited partnership to purchase an inner city apartment building, with each contributing either $6,000 or $12,000. If the partnership raised $522,000, then how many investors contributed $6,000 and how many contributed $12,000? $6,000 investors $12,000 investors Show My Work (optional) a

Explanation / Answer

Let the number of people investing 6000$ is x

Let the number of people investing 12000$ is y

x + y = 60 ---- (i)

6000x + 12000y = 522000 --- (ii)

using elimination substituting x = 60 - y in the second equation

6000(60-y) + 12000y = 522000

360-6y + 12y = 522

6y = 162

y = 162/6 = 27

Hence the number of people investing 6000$ is equal to 33 and number of people investing 12000$ is 27

b)

1 nickel = 5 pennies

1 dime = 10 pennies

Let the number of nickel be x

Let the number of dimes be y

x + y = 70

5x + 10y = 580

substituting x = 70 - y

5(70-y) + 10y = 580

350 + 5y = 580

5y = 230

y = 46

Hence the number of dimes are 46 and number of pennies are equal to 24

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