Question

Sam is 4 years younger than Amy. Five years ago he was half her age. How old are they now?

Answer 1

Answer:

Sam is 9 and Amy is 13

Step-by-step explanation:

Sam = Amy - 4

Sam - 5 = (Amy - 5) / 2  --> 2Sam - 5 = Amy

System of Equation:

2S - 5 = A

S + 4 = A

So,

S + 4 = 2S - 5

S = 9

A = 13

Answer 2

$\bold{given :} \\ \\ sam \:\: is \:\: 4 \: \:yrs \: \:younger \:\: than \: \:amy \\ \\ \\ \\ \bold{let : } \\ \\\bold{ age \: of \: sam :} \\ \\ \bold{x \: yrs \: }\\ \\ \\ \\ \bold{ age \: of \: amy :} \\ \\ \bold{x + 4 \: yrs}$
$\\ \\ \\ \\\bold{five \: yrs \: ago :} \\ \\ age \: of \: sam : \\ \\\bold{ x - 5 \: yrs} \: \\ \\age \: of \: amy : \\ \\ x + 4 - 5 \: \\ \\\bold{ x - 1 \: yr}$
$according\: to \:the \:condition\\ \\ \bold{x - 5 = \frac{1}{2} \times x - 1 }\\ \\ 2(x - 5) = x - 1 \\ \\ 2x - 10 = x - 1 \\ \\ 2x - x = - 1 + 10 \\ \\ \bold{x = 9 \: yrs}$
$\bold{age \: of \: sam \: :} \\ \\ \bold{9 \: yrs \: } \\ \\ \\ \\ \bold{age \: of \: amy : }\\ \\ x + 4 \: yrs \\ \\ 9 + 4 \: yrs \\ \\ \bold{13 \: yrs }$