A contractor prepares a concrete mixture by combining cement, sand, and gravel in a ratio … — ACT

A contractor prepares a concrete mixture by combining cement, sand, and gravel in a ratio of $2 : 3 : 5$ by weight. The contractor currently has a batch of this mixture weighing $150\text{ pounds}$ . If the contractor adds $10\text{ pounds}$ of pure cement to this batch, what fraction of the total weight of the modified mixture is cement?

A
$\frac{1}{5}$
B
$\frac{3}{40}$
$\frac{1}{4}$ Cevap
D
$\frac{4}{15}$
E
$\frac{1}{3}$

Cevap

The fraction of the total weight of the modified mixture that is cement is

\frac{1}{4}

In the original ratio of

2 : 3 : 5

, there are

10

total parts. Cement accounts for

\frac{2}{10} = \frac{1}{5}

of the initial

150\text{-pound}

mixture, which is

30\text{ pounds}

. When

10\text{ pounds}

of cement is added, the new cement weight becomes

40\text{ pounds}

and the total mixture weight increases to

160\text{ pounds}

. The fraction of cement in the modified mixture is

\frac{40}{160} = \frac{1}{4}

Adım Adım Çözüm

Calculate the total ratio parts and the initial amount of cement in the mixture.

Total ratio parts =

2 + 3 + 5 = 10

. Initial cement weight =

\frac{2}{10} \times 150 = 30\text{ pounds}

Determining the weight of cement in the original

150\text{-pound}

batch is necessary before adding extra cement.

Determine the new weight of cement and the new total weight after adding

10\text{ pounds}

of cement.

New cement weight =

30 + 10 = 40\text{ pounds}

. New total weight =

150 + 10 = 160\text{ pounds}

Adding pure cement increases both the weight of the cement component and the total weight of the batch.

Form the part-to-whole ratio for the new mixture and simplify the fraction.

\frac{40}{160} = \frac{1}{4}

The fraction of cement relative to the whole mixture is found by dividing the new cement weight by the new total weight.

Anahtar Kavram

Part-to-whole ratios and adjusting totals when components are added

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Cevap

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