Question

John can answer 45 math questions every 30 minutes. Minutes Number of math questions

30	45
10	$x$
$y$	90

Complete the table using equivalent ratios.

$\text{The value of x}=$

$\text{The value of y}=$

Answer 1

Let the missing numbers are x and y, then

Minutes	Number of math questions
30	45
10	x
y	90

$30:45::2:3$
As, ratios in the given table are equivalent.

Hence, ratio in the second row is also equivalent to $2:3.$
$\Rightarrow 10:x::2:3$
$\Rightarrow \frac{10}{x}=\frac{2}{3}$

Cross multiplying, we get

$\Rightarrow 10\times 3=x\times 2$
$\Rightarrow 30=x\times 2$

Dividing both the sides by $2,$ we get
$\frac{30}{2}=\frac{x\times 2}{2}$
$\Rightarrow 15=x\Rightarrow x=15$

Similarly, $y:90::2:3$
$\Rightarrow \frac{y}{90}=\frac{2}{3}$
Cross multiplying, we get

$y\times 3=90\times 2$
$\Rightarrow y\times 3=180$

Dividing both the sides by $3,$ we get
$\frac{y\times 3}{3}=\frac{180}{3}$
$\Rightarrow y=60$

Hence, the missing numbers are $15$ and $60$ respectively.