You find 66 coins consisting only of nickels, dimes, and quarters, with a face value of $11.55. However, the coins all date from 1919 and are worth considerably more than their face value. A coin dealer offers you $10 for each nickel, $20 for each dime, and $15 for each quarter, for a total of $945. How many nickels did you find? Group of answer choices

You find 19 nickels.

Step-by-step explanation:

This question can be solved using a system of equations.

I am going to say that:

x is the number of nickels.

y is the number of dimes.

z is the number of quarters.

66 coins

This means that x + y + z = 66.

With a face value of $11.55.

Nickel is worth $0.05, dime worth $0.1 and quarter worth $0.25. So

0.05x + 0.1y + 0.25z = 11.55.

A coin dealer offers you $10 for each nickel, $20 for each dime, and $15 for each quarter, for a total of $945.

This means that 10x + 20y + 15z = 945.

How many nickels did you find?

We have to find x.

From the first equation:

z = 66 - x - y

Replacing in the second:

0.05x + 0.1y + 0.25z = 11.55.

0.05x + 0.1y + 0.25(66 - x - y) = 11.55

0.05x + 0.1y + 16.5 - 0.25x - 0.25y = 11.55

0.2x + 0.15y = 4.95

So

0.15y = 4.95 - 0.2x

y = 33 - 1.33x

On the final equation:

10x + 20y + 15z = 945

10x + 20(33 - 1.33x) + 15(66 - x - (33 - 1.33x)) = 945

10x + 660 - 26.6x + 15(66 - x - 33 + 1.33x) = 945

-16x + 660 + 15(33 + 0.33x) = 945

-16x + 660 + 495 + 5x = 945

11x = 210

x = 210/11

x = 19

You find 19 nickels.

ans789

step-by-step explanation:

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet