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?

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.