At open skate night, admission is $3.75 with a membership card and $5.00 without a membership card. Skate rentals are $3.00.
The Moores and Cotters were at open skate night. The Moores paid $6.00 more for skate rentals than the Cotters did. Together, the two families paid $30 for skate rentals. How many pairs of skates did the Moores rent?
Answer (3)
To determine how many pairs of skates the Moores rented, we used the given information to set up equations representing the cost of skate rentals for both families and solved for the number of pairs, which is 6 pairs of skates for the Moores. ;
Let's assume that the Moores rented 'x' pairs of skates and the Cotters rented 'y' pairs of skates.
The Moores paid $6.00 more for skate rentals than the Cotters did, so we can write the equation x * 3.00 = y * 3.00 + 6.00.
Together, the two families paid $30, so we can also write the equation x * 3.75 + y * 5.00 = 30.00.
To solve these equations, we can use substitution or elimination. Let's use elimination:
Multiply the first equation by 5.00 and the second equation by 3.00 to make the coefficients of 'y' the same in both equations.
Subtract the second equation from the first equation to eliminate 'y'.
Solve for 'x'.
Substitute the value of 'x' into one of the original equations to solve for 'y'.
The solution is 'x = 2' and 'y = 4'. Therefore, the Moores rented 2 pairs of skates.
The Moores rented 6 pairs of skates. This was determined by setting up equations based on their rental costs and solving the system. The calculations confirmed that the totals matched the conditions given in the problem.
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