prsategazd

2021-12-26

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

Bukvald5z

Approach.
The quotient of two numbers is called a ratio.
Ex:
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: $ps=rq$
Two variables are said to be directly proportional or varies directly, if their ratio is a constant.
Ex: $\frac{a}{b}=k,a=kb$ where k is a constant.
Two variables are said to be inversely proportional or varies inversely, if their product is a constant.
Ex: $ab=k,a=\frac{k}{b}$ where k is a constant.
Variable a is said to be jointly proportional with b and c means $a=kbc$ 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.
$3×21=7×x$
$63=7x$
$x=\frac{63}{7}$
$x=9$ 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

Step 1
Given:
$\frac{3}{8}=\frac{x}{21}$
Multiply both sides by 21.
$\frac{3}{7}×21=x$
Express $\frac{3}{7}×21$ as a single fraction.
$\frac{3×21}{7}=x$
Multiply 3 and 21 to get 63
$\frac{63}{7}=x$
Divide 63 by 7 to get 9.
$9=x$
Swap side so that all variable terms are on the left hand side
$9=x$

karton

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

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