Answer:
There are 22 $10 coins and 21 $20 coins.
Explanation:
Let x = the number of $10 coins
Let y = the number of $20 coins
You have two unknows so you need two equations.
x + y = 43
10x + 20y = 640.
Rewrite the first equation solving for x
x + y = 43
x = 43 - y Substitute 43 - y in for x in the second equation.
10x + 20 y = 640
10(43 - y) + 20y = 640
430 - 10y + 20y = 640 Subtract 430 from both sides of the equation
-10y + 20y = 210 Combine the y's
10y = 210 Divide both sides by 10
y = 21 This is the number of $20 coins.
Substitute 21 in for y in either of the original equations to solve for x
x + 21 = 43 Subtract 21 from both sides
x = 22 This is the number of $10 coin.
Check:
Substitute in 21 for y and 22 for x
x + y = 43
21 + 22 = 43
43 = 43 checks
10x + 20y = 640
10(22) + 20(21) = 640
220 + 420 = 640
640 = 640 Checks