A design on the surface of a balloon is 5 cm wide when the balloon holds 71 cm of air. How much air does the balloon hold when the design is 10 cm wide? Explain the method you use to find the amount of air.
To find the amount of air the balloon holds when the design is 10 cm wide, we can set up a proportion using the given information.
Let's denote "x" as the unknown amount of air the balloon holds when the design is 10 cm wide.
We know that when the design is 5 cm wide, the balloon holds 71 cm of air. So we can set up the following proportion:
5 cm (design width) : 71 cm (air volume) = 10 cm (design width) : x cm (air volume)
To solve this proportion, we can use cross-multiplication. Multiply 5 cm and x cm, and multiply 71 cm and 10 cm:
5x = 710
Now, isolate "x" by dividing both sides of the equation by 5:
x = 710 / 5
Calculating this, we find that x = 142 cm.
Therefore, when the design is 10 cm wide, the balloon holds 142 cm of air.