The trick here is to relate the NUMBER of coins to each other in one equation, and then the VALUE of the coins in another equation. If I have 1 dime, that 1 dime is worth 10 cents. The number of dimes is obviously not equal to the value. Let's call quarters q and dimes d. The number of these 2 types of coins added together is 80 coins. So q + d = 80. Now, we know that quarters are worth .25 and dimes are worth .1, so we express a quarter's worth as .25q; we express a dime's worth as .1d. The value of the coins we have is 14.90. So that equation is .25q + .1d = 14.90. Let's solve the first equation for q. q = 80 - d. We can now use that as a substitution for q into the second equation, giving us an equation with only 1 unknown, d. .25(80-d) + .1d = 14.90. Distributing through the parenthesis we have 20 - .25d + .1d = 14.90. Combining like terms gives us - .15d = - 5.1. We will divide both sides by - .15 to get that the number of dimes is 34. If we had a total of 80 coins, then the number of quarters is 80 - 34, which is 46. 46 quarters and 34 dimes
Pythagoras:
sqrt( 9^2+12^2) = sqrt( 81+144) = sqrt(225) = 15! Voila :)
Solve both sides and check to see if the solutions match.
(10 • 2) = 20
20 • 3 = 60
Now check the other side:
(2 • 3) = 6
10 • 6 = 60
Compare the solutions:
60 = 60
This is true, so the answer is A. True.
