Question #cb6b4

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Answer 1 · 2017-11-22T20:35:14

smaller number (a): 5.5
bigger number (b): 17.5

The trick with these sorts of question is translating all the messy words into maths.

difference between two numbers is 12: $b - a = 12$ $b-a=12$

larger number + 5 $\times$ $times$ smaller number =45: $b + 5 a = 45$ $b+5a=45$

Now rearrange an equation so it's in terms of one variable, and substitute into the other equation:

$b = 12 + a$ $b=12+a$

Sub this value for $b$ $b$ into the other equation and solve for $a$ $a$ :

$(12 + a) + 5 a = 45$ $(12+a)+5a=45$
$12 + 6 a = 45$ $12+6a=45$
$6 a = 33$ $6a=33$
$a = \frac{33}{6}$ $a=33/6$ or $5.5$ $5.5$

Now put this value for $a$ $a$ back into the first equation, $b - a = 12$ $b-a=12$
$b - 5.5 = 12$ $b-5.5=12$
$b = 17.5$ $b=17.5$