escamillayensi
Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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 appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.