Number problems II

Number sentences

Like we saw earlier, we can use symbols and variables to turn wordy number problems into number sentences or equations. Most of the time, replacing words with symbols gives us a clearer and more succinct expression.

What if I know that the sum of a number and $3$3is $16$16? In words, I would say:

The sum of a number and $3$3 is $16$16

Or I could assign a variable (or variable) to this unknown number, calling it $x$x, and use maths to rewrite the expression as a number sentence:

$x+3=16$x+3=16

Key words

The key to writing equations like this is to be able to identify key words in the sentences.

 

Is it addition or subtraction?

more, sum, add, join, altogether, in total, both, combined, increase are all words that indicate the operation of addition.

left, subtract, minus, remain, decrease, use, less than, difference, take away, fewer, shorter are all words that indicate the operation of subtraction.

 

Is it multiplication or division?

product of, multiplied by, times, of, double, triple, groups are all words that would indicate the operation of multiplication.

quotient of, divided by, per, into, out of , ratio of, unit price, cut up, separated , share equally, split, half, parts are all words that would indicate the operation of division.

is, are, was,were, will be, gives, yields, sold for are all words that would indicate an equals sign.

Mathematising sentences (turning words into maths) is a bit like translating them into another language! But it does get easier with practice.

 

Example

Making maths out of cricket balls

What if we knew that cricket balls cost $99$99 cents more that rugby balls? We could call the cost of a cricket ball $c$c and the cost of a rugby ball $r$r, and use maths to write:

$c=r+0.99$c=r+0.99

Then, if we knew that a cricket ball costs $\$2.25$$2.25 we can write our equation like this:

$2.25=r+0.99$2.25=r+0.99

If we want to find the cost of the rugby ball then we will need solve the equation.

$2.25$2.25	$=$=	$r+0.99$r+0.99
$2.25-0.99$2.25−0.99	$=$=	$r$r
$r$r	$=$=	$1.26$1.26

So a rugby ball costs $\$1.26$$1.26

Examples

Question 1

$x$x divided by $20$20 equals $5$5. Construct an equation and solve for $x$x.

 

Question 2

The product of $5$5 with the sum of $x$x and $7$7 is $50$50. Construct an equation and solve for $x$x.

 

Question 3

The sum of four consecutive odd numbers is $64$64.

a) Let $x$x be the smallest of the numbers. Form an equation and solve for $x$x.

 

b) Find all 4 numbers.