Alec makes jam to sell at a local farmers' market. To make last week's batch, he used 2 cups of sugar and 18 cups of berries. It was so popular that he made a larger batch this week. To make this week's batch, Alec used 4 cups of sugar and 30 cups of berries, and the jam sold out even faster. Which batch had a greater ratio of sugar to berries?
Question
Alec makes jam to sell at a local farmers' market. To make last week's batch, he used 2 cups of sugar and 18 cups of berries. It was so popular that he made a larger batch this week. To make this week's batch, Alec used 4 cups of sugar and 30 cups of berries, and the jam sold out even faster. Which batch had a greater ratio of sugar to berries?
Solution
To determine which batch had a greater ratio of sugar to berries, we need to calculate the ratio for each batch separately.
For the first batch, the ratio of sugar to berries is 2 cups of sugar to 18 cups of berries. To simplify this ratio, we divide both numbers by the greatest common divisor, which is 2. This gives us a ratio of 1:9.
For the second batch, the ratio of sugar to berries is 4 cups of sugar to 30 cups of berries. To simplify this ratio, we divide both numbers by the greatest common divisor, which is 2. This gives us a ratio of 2:15.
To compare these ratios, we can convert them to fractions and see which one is larger. The first ratio, 1:9, is equivalent to 1/9, and the second ratio, 2:15, is equivalent to 2/15.
If we compare these fractions, we can see that 1/9 is larger than 2/15. Therefore, the first batch had a greater ratio of sugar to berries.
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