Final answer:
To find the ratio of Sally's coins to Bill's coins after they each double the number of coins they have, first determine their current number of coins using the given ratio. Sally has 32 coins and Bill has 56 coins. After doubling their coins, Sally will have 64 coins and Bill will have 112 coins. The new ratio of Sally's coins to Bill's coins is 8:14.
Step-by-step explanation:
To find the ratio of Sally's coins to Bill's coins after they each double the number of coins they have, we first need to determine the number of coins they each currently have. From the given information, we know that the ratio of Sally's coins to Bill's coins is 4:7. Let's assume Sally has 4x coins and Bill has 7x coins. So, Sally currently has 4x = 32 coins, which means x = 8. Therefore, Bill currently has 7x = 7 * 8 = 56 coins.
If both Sally and Bill double the number of coins they have, Sally will have 2 * 4x = 8x coins and Bill will have 2 * 7x = 14x coins. Let's substitute x = 8 again to find the new ratio. Sally will have 8 * 8 = 64 coins and Bill will have 14 * 8 = 112 coins. So, the new ratio of Sally's coins to Bill's coins is 64:112, which can be simplified to 8:14. Therefore, after they each double the number of coins they have, the ratio of Sally's coins to Bill's coins is 8:14.