To solve: The proportion for the ratio of lime to sand in mortar

Question

To solve:  The proportion for the ratio of lime to sand in mortar

Bukvald5z · Accepted Answer

Approach.
The quotient of two numbers is called a ratio.
Ex:

\frac{5}{8} or 5 : 8

An equation indicating that two ratios are equal is called a proportion.
Ex:

\frac{3}{4} = \frac{15}{20}, \frac{p}{q} = \frac{r}{s}

In the proportion

\frac{p}{q} = \frac{r}{s}

, the numbers p and s are called extremes, and the numbers r and q are called the means.
In any proportion, the product of the extremes is equal to the product of the means.
Ex:

p s = r q

Two variables are said to be directly proportional or varies directly, if their ratio is a constant.
Ex:

\frac{a}{b} = k, a = k b

where k is a constant.
Two variables are said to be inversely proportional or varies inversely, if their product is a constant.
Ex:

a b = k, a = \frac{k}{b}

where k is a constant.
Variable a is said to be jointly proportional with b and c means

a = k b c

where k is a constant.
Given:
The ratio of lime to sand in mortar is 3:7.
Calculation:
Let the number of bags of lime be x.
Set the proportion, if there are 21 bags of sand to make mortar and solve for no of lime bags x.

\frac{3}{7} = \frac{x}{21}

By property of proportions, the product of the extremes is equal to the product of the means.

3 \times 21 = 7 \times x

63 = 7 x

x = \frac{63}{7}

x = 9

bags
Therefore, number of lime bags that must be mixed with 21 bags of sand to make mortar are 9 bags.
Final statement:
The no of lime bags that must be mixed with 21 bags of sand to make mortar are 9 bags.

Steve Hirano · Accepted Answer

Step 1  Given:  38=x21  Multiply both sides by 21.  37×21=x  Express 37×21 as a single fraction.  3×217=x  Multiply 3 and 21 to get 63  637=x  Divide 63 by 7 to get 9.  9=x  Swap side so that all variable terms are on the left hand side  9=x  Answer: 9

karton · Accepted Answer

Step 1
Solution by Cross Multiplication
For the equation
$\frac{3}{7} = \frac{x}{21}$
The cross product is
$3 \times 21 = 7 \times x$
Solving for x
$x = \frac{3 \times 21}{7}$
and reducing
$x = 9$
Step 2
Solution by Proportion
Since the equation is an equality
If
$21 \div 7 = 3$
Then it is true that
$x \div 3 = 3$
Solving for x
$x = 3 \times 3$
$x = 9$

To solve: The proportion for the ratio of lime to sand

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