Question

1. multiselect one blend of garden soil is 1 part minerals, 1 part peat moss, and 2 parts compost. select all of the mixtures below that are in a proportional relationship with this blend. 5 ft³ minerals, 5 ft³ peat moss, 10 ft³ compost 10 ft³ minerals, 15 ft³ peat moss, 15 ft³ compost 12 ft³ minerals, 12 ft³ peat moss, 24 ft³ compost 20 ft³ minerals, 20 ft³ peat moss, 40 ft³ compost 100 ft³ minerals, 100 ft³ peat moss, 200 ft³ compost 50 ft³ minerals, 50 ft³ peat moss, 50 ft³ compost

Explanation:

Step1: Identify the ratio

The original blend ratio is minerals : peat moss : compost = \(1:1:2\) (since 1 part minerals, 1 part peat moss, 2 parts compost).

Step2: Check each option

• Option 1: \(5\,\text{ft}^3\) minerals, \(5\,\text{ft}^3\) peat moss, \(10\,\text{ft}^3\) compost

Ratio: \(5:5:10 = 1:1:2\) (divide by 5). Matches.

• Option 2: \(10\,\text{ft}^3\) minerals, \(15\,\text{ft}^3\) peat moss, \(15\,\text{ft}^3\) compost

Ratio: \(10:15:15 = 2:3:3\). Does not match \(1:1:2\).

• Option 3: \(12\,\text{ft}^3\) minerals, \(12\,\text{ft}^3\) peat moss, \(24\,\text{ft}^3\) compost

Ratio: \(12:12:24 = 1:1:2\) (divide by 12). Matches.

• Option 4: \(20\,\text{ft}^3\) minerals, \(20\,\text{ft}^3\) peat moss, \(40\,\text{ft}^3\) compost

Ratio: \(20:20:40 = 1:1:2\) (divide by 20). Matches.

• Option 5: \(100\,\text{ft}^3\) minerals, \(100\,\text{ft}^3\) peat moss, \(200\,\text{ft}^3\) compost

Ratio: \(100:100:200 = 1:1:2\) (divide by 100). Matches.

• Option 6: \(50\,\text{ft}^3\) minerals, \(50\,\text{ft}^3\) peat moss, \(50\,\text{ft}^3\) compost

Ratio: \(50:50:50 = 1:1:1\). Does not match \(1:1:2\).

Answer:

A. \(5\,\text{ft}^3\) minerals, \(5\,\text{ft}^3\) peat moss, \(10\,\text{ft}^3\) compost
C. \(12\,\text{ft}^3\) minerals, \(12\,\text{ft}^3\) peat moss, \(24\,\text{ft}^3\) compost
D. \(20\,\text{ft}^3\) minerals, \(20\,\text{ft}^3\) peat moss, \(40\,\text{ft}^3\) compost
E. \(100\,\text{ft}^3\) minerals, \(100\,\text{ft}^3\) peat moss, \(200\,\text{ft}^3\) compost