Final answer:
Using the ratio of 9 sports drinks to 5 sodas and knowing that 126 sports drinks were sold, we calculated the proportion and found that 70 sodas were sold.
Step-by-step explanation:
The question pertains to the ratio of sports drinks to sodas sold from a vending machine, which is given as 9:5. Given that there were 126 sports drinks sold, we can use this ratio to find the number of sodas sold.
To determine the number of sodas sold based on the given ratio, we first need to understand that for every 9 sports drinks sold, 5 sodas are sold. This sets up a proportion where if 9 sports drinks are equated to 126 sports drinks sold, then we can find the equivalent number of sodas by cross-multiplication.
Steps to calculate the number of sodas sold:
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- Set up the ratio as a proportion: (9 sports drinks / 5 sodas) = (126 sports drinks / x sodas).
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- Cross-multiply to solve for x: 9x = 5 * 126.
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- Divide both sides by 9 to find x: x = (5 * 126) / 9.
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- Calculate x to find the number of sodas sold.
When we compute the value of x, we get:
x = (5 * 126) / 9
x = 630 / 9
x = 70
Therefore, the vending machine sold 70 sodas.