Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

sally has 20 coins in her piggy bank,all dimes and quarters. The total amount of money is $3.05. How many of each coin does she have?

Sagot :

let d = number of dimes, q = number of quarters 

Sally has 20 coins in her piggy bank, so 
d + q = 20 

The total amount of money is $3.05. 
Use the value of each coin multiplied by its number to get total value 
.10d + .25q = 3.05 
multiply everything by 100 to clear the decimal places 
10d + 25q = 305 and 
d + q = 20 

solve the second equation above in terms of either d or q - lets do d 
d = 20 - q 
sub that into the first equation 
10d + 25q = 305 
10(20 - q) + 25q = 305 
200 - 10q + 25q = 305 
15q = 105 
q = 105/15 = 7 
and from above 
d = 20 - q = 20 - 7 = 13 

so, there are 13 dimes and 7 quarters 
verify with orig problem 
13 + 7 = 20, OK, and $1.30 + $1.75 = $3.05 

luana
[tex]x-\ amount\ of\ dimes\\\\y-\ amount\ of\ quarters\\\\ \left \{ {{x+y=20} \atop {0,1x+0,25y=3,05\ \ |*(-10)}} \right.\\\\ \left \{ {{x+y=20} \atop {-x-2,5y=-30,5}} \right. \\+-----\\Addition\\\\ -1,5y=-10,5\ \ \ | divide\ by\ -1,5\\\\ y=7\\\\x=13\\\\There\ are\ 7\ quarters\ and\ 13\ dimes.[/tex]
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.