Question

lilli has $3.65 comprised of quarters and dimes floating on the bottom of her bag she has five more dimes than twice her quarters how many each type of coin does she have? lol pls help

Answer 1

Answer:

= 3.65.

Step-by-step explanation:

You know that Tom has 23 coins in total. That means the number of dimes and the number of quarters equals 23.

D + Q = 23

You also know that the total value of the coins is $3.65. A dime is worth $0.10 and a quarter is worth $0.25, so:

0.10*D + 0.25*Q = 3.65

That says that 10 cents per dime times the number of dimes, plus 25 cents per quarter times the number of quarters is three dollars and sixty-five cents.

So you have a system of linear equations:

D + Q = 23

0.10D + 0.25Q = 3.65

I'm going to multiply the bottom row by 100 to clear the decimals.

D + Q = 23

10D + 25Q = 365

Now I can multiply the top row by -10 to eliminate the D terms

-10D - 10Q = -230

10D + 25Q = 365

________________

0D + 15Q = 135

15Q = 135

Q = 9

Tom has 9 quarters.

If D + Q = 23, and Q = 9, then:

D + 9 = 23

D = 14

Tom has 14 dimes.

Always good to double check:

9 quarters is worth $2.25. 14 dimes is worth $1.40. These should sum to $3.65.

2.25 + 1.40