Equations

UK Secondary (7-11)

Formulas, substitution and equations I

Lesson

Out in the real world all sorts of amazing relationships play out every day: Air temperatures change with ocean temperatures. Populations of species rise and fall depending on seasons, food availability and the number of predators. The surface area of a human body can even be measured fairly accurately according to your height and weight.

One of the most powerful things about mathematics is its ability to describe and measure these patterns and relationships exactly. Given a mathematical formula for the relationship between, say, the weight of a patient and how much medication they should be given, we can find one quantity by substituting a value for the other.

We have come across so many different formulae in mathematics that allow us to measure quantities such as Area, Volume, Speed etc. Let's have a look at the process of substituting values into these formulae to find a particular unknown.

The perimeter of a triangle is defined by the formula $P=x+y+z$`P`=`x`+`y`+`z`. Find $P$`P` if the length of each of its three sides are $x=5$`x`=5 cm, $y=6$`y`=6 cm and $z=3$`z`=3 cm.

**Solution**:

By inserting the number values of $x$`x`, $y$`y` and $z$`z` we have a new equation that we can use to find the value of $P$`P`:

$P=5+6+3$`P`=5+6+3

$P=14$`P`=14 cm

The area of a square with side $a$`a` is given by the formula $A=a^2$`A`=`a`2. Find $A$`A` if $a=6$`a`=6 cm.

**Solution**:

From the information above, we know that we are finding the area of a square where each side measures $6$6cm.

Substituting our value for $a$`a` into the formula:

$A=6^2$`A`=62

$A=36$`A`=36 $cm^2$`c``m`2

Now let's have a look at a worked video solution.

The simple interest generated by an investment is given by the formula $I=\frac{P\times R\times T}{100}$`I`=`P`×`R`×`T`100.

Given that $P=1000$`P`=1000, $R=6$`R`=6 and $T=7$`T`=7, find the interest generated.