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24 votes
There are 30 coins all dimes and quarters on the table worth$5.10. How many quarters are there?

User Nicolas Finelli
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1 Answer

26 votes
26 votes

Let's set the following variables:

x= number of quarters

y= number of dimes

The question states there are 30 coins in total, thus:

x+y=30 [1]

Since each quarter is worth $0.25 and each dime is worth $0.10, the total money on the table is:

0.25x+0.10y=5.10 [2]

The equations [1] and [2] form a system that can be solved in several ways. Let's do it by the substitution method

From equation [1], we solve for x:

x=30-y

Now we substitute x into equation [2]:

0.25(30-y)+0.10y=5.10

Operate the parentheses:

7.5-0.25y+0.10y=5.10

Joining like terms:

-0.15y=5.10-7.5

Operating again:

-0.15y=-2.4

Solving:

y=(-2.4)/(-0.15)=16

Now we use this value to find x:

x=30-y=30-16=14

Thus, there are 14 quarters and 16 dimes

User Osama Gamal
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