A collection of dimes and quarters is worth $6.50. There are 35 coins in all. How many dimes are there?

Write the correct systems of equation and solve

Question

A collection of dimes and quarters is worth $6.50. There are 35 coins in all. How many dimes are there? 

Write the correct systems of equation and solve

anonymous · Answer

Say you have x dimes that are worth 0.1 each
and 35 - x quarters that are worth 0.25 each
0.1x + 0.25(35-x) = 6.50
Solve for x and you get the number of dimes. 
Let us know what you come up with.

sburchette · Answer

You can let x=number of quarters and y=number of dimes. Based on the information in the question, we know that the total number is 35 and that the change adds up to 6.50. One equation we can form is $$x+y=35$$because the total number of coins is 35. The other equation is $$.25x+.1y=6.5$$Because the number of dimes times their value plus the number of quarters times their value gives us a total of 6.5. Now we can solve for x or y easily in the first equation, so I would use substitution. Solving for y$$y=35-x$$We can substitute this into the other equation to obtain$$.25x+.1(35-x)=6.5$$This simplifies to$$.15x+3.5=6.5$$$$.15x=3$$$$x=20$$We can now substitute x=20 into the first equation to find y. If x+y=35, then 20+y=35. So y=15 We can conclude that there were 20 quarters and 15 dimes.

ledah · Answer

great job on that explanation by the way. and these are just fun problems for people to solve