Sue has $1.15 in nickels and dimes, a total of 16 coins. how many nickels and how many dimes does sue have? , i have 10 minutes to solve

0.05x+0.10y=1.15
x+y=16
solve the system

Hey :)

Lets n be the number of nickels Sue has. Then the number of dimes is equal to (16-n). So, Sue has 5*n cents in nickels and 10*(16-n) cents in dimes. Since the total amount Sue has is $1.15, or 115 cents, it gives you an equation 5n + 10*(16-n) = 115.

Simplify this equation: 5n +160-10n = 115 (after opening parentheses) -5n = 115-160 (after collecting like terms at the left side and moving 160 to the right side with the opposite sign) -5n = -45 (after collecting like terms at the right side) n = 9 (after dividing both sides by -5). So, the number of nickels is equal to 9. The number of dimes is equal to 16 minus the number of nickels, that is 16-n = 16-9 = 7.

Check. The total number of coins is equal to 9 + 7 = 16. The total amount is equal to 9*5 + 7*10 = 45 + 70 = 115. The solution is correct.

Answer. Sue has 9 nickels and 7 dimes.

Hope this helps! :)