Lizbeth has 38 coins consisting of nickels, dimes, and quarters. The total value of the coins is $6.40. The number of quarters if three more than three times the number of dimes. How many of each type of coin does Lizbeth have? PLEASE EASY 25 POINTS.

21 quarters, 6 dimes, and 11 nickels

Step-by-step explanation:

# of Quarters = x.

# of Dimes = y.

# of Nickels = z.

(i)x = 3y+3.

(ii) 0.25x + 0.1y + 0.05z = 6.4

(iii) x + y + z = 38.

Multiplying (iii) by -0.05, and adding it to (ii),

we then get:

0.2x + 0.05y = 4.5.

Now plug in (i) into this.

0.65y + 0.6 = 4.5.

0.65y = 3.9

y = 6.

Since y = 6, we can subsitute this into our equation.

0.2x + 0.3 = 4.5

0.2x = 4.2

x = 21.

Since x = 21, y =6, then z = 11.

d. corresponding side lengths in similar triangles are proportional in length.

step-by-step explanation: