Question

A woman has 21 coins in her pocket, all of which are dimes and quarters. if the total value of the coins is $ 3.30, how many dimes and how many quarters does she have?

Answer 1

Let,
d↪no of dimes
q ↪no of quarters

1st condition:
d+q=21..........(i)

1 dime=$(1/10) ➡'d' no of dimes =$ (d/10)
1 quarter=$(1/4)➡'q' no of quarters =$ (q/4)

2nd condition:
$(d/10)+ $(q/4)=$3.30
or, (d/10)+ (q/4)=3.30
or, (2d+5q)/20=3.30
or, 2d+5q=3.30 × 20
or,2d+5q=66...........(ii)

Multiplying (i) by 2 & subracting (i) from (ii),
[(ii) - 2×(i)]..we get

↪3q=24
↪q=8>>>>>>>>>>>ANS
Thus,
d=21-8
↪d=13>>>>>>>>>>>>ANS

[U can check the answer by putting in (ii)
↪ 13/10+8/4
=1.3+2
=3.30....satisfied]

That means , she have 8 quarters & 13 dimes in her pocket.