Question

An athletic club buys car magnets at $4.95 each and pom-poms at $0.85 each. If the total cost of n car magnets and

m pom-poms is $110, and the total number of items bought is 100, what are the values of n and m?
a) n=20,m=80
b) n=10,m=90
c) n=15,m=85
d) n=25,m=75

Answer 1

n = 20 and m = 466

Step-by-step explanation:

Let's set up the equations based on the given information:

n = number of car magnets

m = number of pom-poms

The cost of n car magnets is $4.95n

The cost of m pom-poms is $0.85m

The total cost of n car magnets and m pom-poms is $110

So we have the equation: $4.95n + $0.85m = $110

We also know that the total number of items bought is 100, so n + m = 100

We can solve this system of equations using substitution or elimination.

Let's use elimination:

Multiply the first equation by 100 to make the coefficients of n in both equations the same:

495n + 85m = 11000

Now subtract the second equation from the first equation:

(495n + 85m) - (100n + 100m) = 11000 - 10000

Simplify:

395n - 15m = 1000

Now we have a system of two linear equations:

495n + 85m = 11000

395n - 15m = 1000

Next, we can use substitution to solve for one variable:

From the second equation, we can solve for n:

n = (1000 + 15m)/395

Now substitute this value of n into the first equation:

495((1000 + 15m)/395) + 85m = 11000

Now we can solve for m:

49500 + 742.46m + 85m = 11000*395

Take out like terms:

742.46m + 85m = 435500 - 49500

Combine like terms:

827.46m = 386000

Divide both sides by 827.46:

m = 466.53

Since m has to be a whole number, it means that m = 466

Now substitute this value of m back into the equation for n:

n = (1000 + 15(466))/395

n = 20

Therefore, the values of n and m are n = 20 and m = 466.