“Alex has $1.65 in nickels and dimes. He has 25 coins in all.”
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5 points
x-y=25 and .05x-.10y=1.65
x+y=25 and .05x+.10y=1.65
-x+y=25 and .05x-.10y=1.65
x-y=25 and -.05x+.10y=1.65
The correct equations are:
x + y = 25 (equation 1) - representing the total number of coins
0.05x + 0.10y = 1.65 (equation 2) - representing the total value of the coins in dollars (converted from nickels and dimes)
Equation 1 represents the total number of coins, which is 25. Since nickels and dimes are two types of coins, the sum of the number of nickels (x) and the number of dimes (y) must equal 25. This gives us the equation x + y = 25.
Equation 2 represents the total value of the coins, which is $1.65. In dollars, a nickel is equal to 0.05, and a dime is equal to 0.10. Therefore, the value of x nickels (0.05x) plus the value of y dimes (0.10y) must equal $1.65. This gives us the equation 0.05x + 0.10y = 1.65.