Question

Sophia has dimes and nickels worth $1.25. If there are 4 more nickels than dimes, how many of each type of coin does Sophia have?


I'll give brainliest to the first correct answer with explanation :))

Answer 1

Solution:-

$\longrightarrow$Let the the number of dimes be x

$\longrightarrow$So, the number of nickels = x+4

(as the number of nickels is four more than dimes)

Now,

$\leadsto$Total amount of money= $ 1.25

$\quad$= 125 cents $\quad$(1 dollar = 100cents)

$\leadsto$Amount of money in dimes(in cents)

$\quad$= 10x $\quad\quad\quad$ (1 dime = 10 cents)

$\leadsto$Amount of money in nickels(in cents)

$\quad$ = 5(x+4) $\quad\quad$(1 nickel = 5 cents)

further,

Total amount of money by nickels and dimes = 125 cents

$\implies$10x+ 5(x+4) = 125

$\implies$10x+5x+20 =125

$\implies$15x + 20 = 125

$\implies$15x = 105

$\implies$x = 7

$\bull$Number of dimes = x = 7

$\bull$Number of nickels = x+4

$\quad$= 7+4

$\quad$= 11

$\green\therefore \quad$Sophia has 7 dimes and 11 nickels.