Question

At Laurita’s Bakery, 3/5 of the baked goods are pies, and the rest are cakes. 1/3 of the pies are coconut. 1/6 of the cakes are angel food.

a. What fraction of all of the baked goods at Laurita’s Bakery are coconut pies?
b. What fraction of all of the baked goods at Laurita’s Bakery are angel food cakes?

Answer 1

1/5 of all baked goods at Laurita's Bakery are coconut pies, and 1/15 are angel food cakes.

Step-by-step explanation:

To determine the fraction of coconut pies and angel food cakes out of all baked goods at Laurita's Bakery, we perform the following calculations:

a. Since 3/5 of the baked goods are pies and 1/3 of those pies are coconut, we multiply the two fractions to find the fraction of all baked goods that are coconut pies:

`\((3)/(5) * (1)/(3) = (3 * 1)/(5 * 3) = (1)/(5)\)`

So, 1/5 of all baked goods are coconut pies.

b. As for the angel food cakes, if the rest of the baked goods are cakes, this means 2/5 of them are cakes (since 1 - 3/5 = 2/5). Then 1/6 of those are angel food, so we multiply:

`\((2)/(5) * (1)/(6) = (2 * 1)/(5 * 6) = (2)/(30) = (1)/(15)\)`

Hence, 1/15 of all baked goods are angel food cakes.

Answer 2

Part a) The fraction of all of the baked goods at Laurita’s Bakery that are coconut pies is 1/5

Part b) The fraction of all of the baked goods at Laurita’s Bakery that are angel food cakes is 1/15

Step-by-step explanation:

Let

x -----> the total number of baked goods

we know that

1) 3/5 of the baked goods are pies and the rest are cakes

To obtain the number of pies multiply the total number of baked goods by 3/5

The number of pies is ----> (3/5)x

To obtain the number of cakes subtract the number of pies from the total number of baked goods

The number of cakes is -----> x-(3/5)x=(2/5)x

2) 1/3 of the pies are coconut

To obtain the number of coconut pies multiply the number of pies by 1/3

The number of coconut pies is -----> (3/5)x(1/3)=(3/15)x=(1/5)x

3) 1/6 of the cakes are angel food

To obtain the number of angel food cakes multiply the number of cakes by 1/6

The number of angel food cakes is -----> (2/5)x(1/6)=(2/30)x=(1/15)x

Part a) What fraction of all of the baked goods at Laurita’s Bakery are coconut pies?

we know that

The number of coconut pies is (1/5)x (see Part 2)

Divide the number of coconut pies by the total number of baked goods

`((1/5)x)/(x)=(1)/(5)`

therefore

The fraction of all of the baked goods at Laurita’s Bakery that are coconut pies is 1/5

Part b) What fraction of all of the baked goods at Laurita’s Bakery are angel food cakes?

we know that

The number of angel food cakes is (1/15)x (see Part 3)

Divide the number of angel food cakes by the total number of baked goods

`((1/15)x)/(x)=(1)/(15)`

therefore

The fraction of all of the baked goods at Laurita’s Bakery that are angel food cakes is 1/15