Question

The sum of two number is 2020 and one of them is one-third the other. Find the number

Answer 1

Answer:

♪＼(*＾▽＾*)／＼(*＾▽＾*)／

Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\underline{ \mathfrak{ \: \: Given, \: \: }} \\ \\ \text{The sum of two number = 2020} \\ \\ \text{One of them is one-third the other.} \\ \\ \underline{ \mathfrak{ \: \:Suppose, \: \: }} \\ \\ \: \: \: \: \text{The numbers are \: \red{x} \: and \: \red{y}.}$

$\underline{ \bold{ \: \: A.T.Q., \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \bold{x + y = 2020 \: \: \: ---->(1) } \\ \\ \text{And,} \\ \\ \: \: \: \: \: \: \: \: \bold{x = \frac{1}{3} \: \: of \: \: y} \\ \\ \bold{ \implies \: x = \frac{1}{3} \times y } \\ \\ \bold{ \implies \: x = \frac{y}{3} \: \: \: \: \: \: \: - - - --->(2) }$

Putting the value of x in eq. (1), we get,

$\tt{(1)\implies \: x + y = 2020 }\\ \\ \: \: \: \: \: \: \: \tt{\implies \: (\frac{y}{3} ) + y = 2020 }\\ \\ \: \: \: \: \: \: \: \tt{ \implies \: \frac{y + 3y}{3} = 2020} \\ \\ \: \: \: \: \: \: \: \tt{\implies \: \frac{4y}{3} = 2020 }\\ \\ \: \: \: \: \: \: \: \tt{\implies \: 4y = 2020 \times 3} \\ \\ \: \: \: \: \: \: \: \tt{\implies \:4y = 6060} \\ \\ \: \: \: \: \: \: \: \tt{\implies \:y = \frac{6060}{4} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{\therefore \: \red{y = 1515}}$

Putting the value of y in eq. (2), we get,

$\tt{(2)\implies \: x= \frac{y}{3} } \\ \\ \: \: \: \: \: \: \: \tt{\implies \: x = \frac{1515}{3} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ \therefore \: \red{x = 505}}$

$\: \: \: \: \: \: \: \sf{ \therefore\: \: \red{ x =505 } \: \: \: and \: \: \: \red{y = 1515}}$