Question 135084: The Jaspers collect nickels, dimes, and quarters in a jar. When they count the change in the jar, there are twice as many nickels as there are quarters. If there is $15.30 in dimes and $74.80 in all, how many quarters are there?
Answer by algebrapro18(249)   (Show Source):
You can put this solution on YOUR website! The Jaspers collect nickels, dimes, and quarters in a jar. When they count the change in the jar, there are twice as many nickels as there are quarters. If there is $15.30 in dimes and $74.80 in all, how many quarters are there?
well let n = number of nickels, d be the number of dimes, and q be the number of quarters. Now we need to set up a system of three equations with three unknowns. We know that the total monetary amount in dimes is 15.30 so we get the equation .10d = 15.30 as one of our equations. We also know that there are twice as many nickels as there are quarters. So the equation for this would be 2n = q. we also now that there if you add up all the change in the jar there is $74.80 In a mathematical equation this becomes .1d + .05n + .25q = 75.80. So now we have our three equations with three unknowns.
.1d + .05n + .25q = 75.80.
2n = q
.10d = 15.30
Now we go about doing the algebra to find how many quarters there are.
solving the third equation we can find out how many dimes there are and we can use this to find how many quarters there are.
.10d = 15.30
d = 153
now we know that there were 153 dimes in that jar. We can use this to rewrite the system and now its a system of two equations with 2 unknowns.
.1(153) + .05n + .25q = 75.80.
2n = q
or simplifying you get
.05n + .25q = 60.50
2n = q
now since you only want to know how many quarters there are you can solve the second equation for n and then plug that into the first equation and solve for q.
2n=q
n = .5q
.05(.5q) + .25q = 60.50
.025q + .25q = 60.50
.275q = 60.50
q = 220
so we know that there are 220 quarters in the jar.
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