Question

mary has 81 coins that have a total value of $5.40. if all of the coins are nickels and dimes how many of each does mary have

Answer 1

54 nickels and 27 dimes

1 dime = 10 cents = $0.1

1 nickel = 5 cents = $0.05

setting up 2 equations

let n = amount of nickels and d = amount of dimes, then

n + d = 81 → (1)

0.05n + 0.1d = 5.4 → (2)

multiply (2 ) by 10

0.5n + d = 54 → (3)

subtract (3) from (1) to eliminate d

0.5n = 27 ( divide both sides by 0.5 )

n =
`(27)/(0.5)` = 54

substitute n = 54 in (1)

54 + d = 81 ( subtract 54 from both sides )

d = 27

Mary has 54 nickels and 27 dimes