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Write an equation to represent ench situation and then solve it to answer the cusstion. A situation may require more than ons equation. (3) A rectangular pool has a width of 24 feet. A second rectangular pool has a perimeter of 48 feet, which is \( \frac{1}{3} \) the perimeter of the first pool. What is the length of the first pool? (4) The local firefighters collect toys to distribute at various give-away events. They have 4569 toys and will sponsor 129 give-away events. How many toys can they give away at each event? How many toys, if any, will be left over?

Ask by Chavez Chambers. in Germany
Mar 09,2025

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**(3) Length of the first pool:** - The first pool is 48 feet long. **(4) Toys per event and leftovers:** - Each event gets 35 toys. - 54 toys are left over.

Solution

**(3) Finding the length of the first pool** Let the length of the first pool be \( L \) feet. The width is given as 24 feet, so the perimeter of the first pool is \[ 2(L+24) \] We are told that a second pool has a perimeter of 48 feet, and that this is \(\frac{1}{3}\) of the perimeter of the first pool. Therefore, we set up the equation: \[ 48 = \frac{1}{3} \times 2(L+24) \] Multiply both sides by 3 to eliminate the fraction: \[ 144 = 2(L+24) \] Divide both sides by 2: \[ 72 = L+24 \] Subtract 24 from both sides: \[ L = 72 - 24 = 48 \] Thus, the length of the first pool is \(\boxed{48\ \text{feet}}\). --- **(4) Dividing toys among events** The firefighters have 4569 toys to distribute among 129 events. Let the number of toys given away per event be \( T \) and the remainder be \( R \). We need to perform the division: \[ 4569 \div 129 \] Perform the division: - Calculate \( 129 \times 35 = 4515 \) - Subtract to find the remainder: \[ 4569 - 4515 = 54 \] So, each event receives \(\boxed{35}\) toys, with a remainder of \(\boxed{54}\) toys left over.

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To find the length of the first pool, we start with the perimeter formula for a rectangle, \( P = 2 \times (length + width) \). The first pool's width is 24 feet, so its perimeter, \( P_1 \), can be expressed as \( P_1 = 2 \times (L_1 + 24) \). The second pool has a perimeter of 48 feet, which is \( \frac{1}{3} \) of the first pool, so \( P_2 = 48 \) and we have \( P_1 = 3 \times 48 = 144 \). Now substituting into the equation for \( P_1 \): \( 144 = 2 \times (L_1 + 24) \) Dividing both sides by 2 gives: \( 72 = L_1 + 24 \) Subtracting 24 from both sides results in: \( L_1 = 72 - 24 = 48 \) Thus, the length of the first pool is 48 feet. For the toy giveaway situation, we need to divide the total number of toys by the number of events. The equation is: \( T = 4569 \div 129 \). Calculating this gives approximately \( T = 35.4 \). Since they cannot give away a fraction of a toy, we round down to 35 toys per event. To find out how many toys will be left over, we multiply the number of events by the number of toys given away per event: \( 129 \times 35 = 4515 \). Finally, we calculate the leftovers: \( 4569 - 4515 = 54 \). So, they can give away 35 toys at each event, with 54 toys left over.

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