Suppose Tom has 24 coins totaling $4.35. If he has only dimes and quarters, how many of each type does he have? Please show work.
In cents, that's 435¢ and dimes = 10¢, quarters = 25¢ each so
q = number of quarters
24 - q = number of dimes
10(24 - q) = value of dimes
25q = value of quarters
25q + 10(24 - q) = 435
25q + 240 - 10q = 435
15q = 435 - 240
15q = 195
so divide 195 by 15 to get q, then plug in to get d.
d + q = 24
10d + 25q = 435
10d + 10q = 240
q = 13
Tom has 11 dimes and 13 quarters.
d + q = 24 & 10 d + 25 q = 435...solve...{ 13 ,11 }
Comments
In cents, that's 435¢ and dimes = 10¢, quarters = 25¢ each so
q = number of quarters
24 - q = number of dimes
10(24 - q) = value of dimes
25q = value of quarters
25q + 10(24 - q) = 435
25q + 240 - 10q = 435
15q = 435 - 240
15q = 195
so divide 195 by 15 to get q, then plug in to get d.
d + q = 24
10d + 25q = 435
10d + 10q = 240
15q = 195
q = 13
Tom has 11 dimes and 13 quarters.
d + q = 24 & 10 d + 25 q = 435...solve...{ 13 ,11 }