To create a specific type of mortar, a builder mixes cement and sand in a ratio of 2 to 5 … — SAT

To create a specific type of mortar, a builder mixes cement and sand in a ratio of $2$ to $5$ by weight. To create a concrete mixture, the builder mixes this mortar with gravel in a ratio of $7$ to $3$ by weight. If the builder prepares $300$ kilograms of the concrete mixture, how many kilograms of sand are needed?

A
90
B
120
150Answer
D
210

Answer

150

To find the weight of the sand needed, first determine the weight of the mortar in the concrete mixture. The ratio of mortar to gravel is

7

3

, meaning mortar represents

\frac{7}{10}

of the total

300

-kilogram concrete mixture. The weight of the mortar is

\frac{7}{10} \times 300 = 210

kilograms. Next, since mortar consists of cement and sand in a ratio of

2

5

, the sand represents

\frac{5}{7}

of the mortar's weight. Calculating

\frac{5}{7}

210

kilograms yields

150

kilograms. Therefore, the weight of the sand needed is

150

kilograms.

Step-by-Step Solution

Find the total weight of the mortar in the concrete mixture.

210

kilograms

The concrete mixture has a ratio of mortar to gravel of

7

3

by weight. This means mortar makes up

\frac{7}{7+3} = \frac{7}{10}

of the total concrete weight. Multiplying this fraction by the total weight of

300

kilograms gives

\frac{7}{10} \times 300 = 210

kilograms of mortar.

Find the weight of the sand within the mortar.

150

kilograms

The mortar is composed of cement and sand in a ratio of

2

5

by weight. Thus, sand makes up

\frac{5}{2+5} = \frac{5}{7}

of the mortar's weight. Multiplying this fraction by the mortar's weight of

210

kilograms yields

\frac{5}{7} \times 210 = 150

kilograms of sand.

Key Concept

Solving multi-step ratio problems by determining part-to-whole relationships and compounding ratios.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic