Question

dave bowers collects U.S gold coins he has a collection of 43 coins.some are $10 coins, and the rest are $20 coins.if the face value of the coins is $660,how many of each denomination does he have?

Answer 1

Number of $10 coins =

Number of $20 coins

STEP - BY - STEP EXPLANATION

What to find?

• Number of $10 coins.

,

• Number of $20 coins.

Given:

• Total number of coins = 43

,

• Total value of coins = $660

To solve the given problem, we will follow the steps below:

Step 1

Translate the given problem into an equation.

Let x be number of $10 coins.

Let y be number of $20 coins.

x + y = 43 -----------------------------------(1)

10x + 20y = 660 ----------------------------------(2)

Step 2

Using substitution method to solve, make x the subject of formula in equation (1).

x= 43 - y

Step 3

Substitute the result in step 2 into equation (2).

`10\mleft(43-y\mright)+20y=660`

Step 4

Open the prenthesis.

`\begin{gathered} 430-10y+20y=660 \\ \\ 430+10y=660 \end{gathered}`

Step 5

Subtract 430 from both-side of the equation.

`\begin{gathered} 10y=660-430 \\ \\ 10y=230 \end{gathered}`

Step 6

Divide both-side of the equation by 10.

`\begin{gathered} (10y)/(10)=(230)/(10) \\ \\ y=23 \end{gathered}`

Step 7

Substitute the value of y into x=43 - y and solve for x.

`\begin{gathered} x=43-23 \\ x=20 \end{gathered}`

Therefore, he has 20 numbers of $10 and 23 numbers of $20.