Question

The ratio of tents at Campsite Windy to tents at Campsite Breezy was 4:7 8 tents were then moved from Campsite Breezy to Campsite Windy. The ratio of tents at Campsite Windy to tents at Campsite Breezy became 6:5. Work out how many tents are now at Campsite Breezy.​

Answer 1

Let's use algebra to solve the problem.

Let's start by representing the number of tents at Campsite Windy and Campsite Breezy before the 8 tents were moved as 4x and 7x, respectively.

After 8 tents were moved from Campsite Breezy to Campsite Windy, the number of tents at Campsite Windy became 4x + 8, and the number of tents at Campsite Breezy became 7x - 8.

Now we know that the ratio of tents at Campsite Windy to tents at Campsite Breezy is 6:5, so we can set up the following equation:

(4x + 8) / (7x - 8) = 6/5

To solve for x, we can cross-multiply to get:

5(4x + 8) = 6(7x - 8)

Simplifying this expression, we get:

20x + 40 = 42x - 48

28x = 88

x = 22/7

Now we can find the number of tents at Campsite Breezy after 8 tents were moved by substituting x = 22/7 into the expression 7x - 8:

7(22/7) - 8 = 6

Therefore, there are now 6 tents at Campsite Breezy.