PLEASE HELP! Riley reached into his pocket and pulled out a total of 27 coins, consisting of quarters and dimes. If the total value of the coins is $5.55, how many quarters does he have?

He has 19 quarters.

Step-by-step explanation:

To solve this, we can set up a system of equations.

Let's first name our variables.

x: number of quarters

y: number of dimes

Using this, we can write the following equations.

Number of coins: x+y=27

Total Value: 0.25x+0.1y=5.55

We can rewrite the first equation to x=27-y by subtracting y from btoh sides. This way, we can substitute 27-y in for x.

0.25(27-y)+0.1y=5.55

Distribute.

6.75-0.25y+0.1y=5.55

Combine like terms.

6.75-0.15y=5.55

Subtract 6.75 from both sides.

-0.15y=-1.2

Divide both sides by -0.15

y=8

There are 8 dimes.

We can use that to find the number of quarters by plugging it in to one of the equations.

x+y=27

x+8=27

Subtract 8 from both sides.

x=19

He has 19 quarters.

you need a common difference between consecutive terms to be constant, like 1,2,3,4 or 2,4,6,8, or 1,3,6,9