Question

Ayesha has only rs.5 and rs.10 coins with her.If the total no. of coins she has is 25 and the amount of money with her is rs.160 , then the no. of rs.5 and rs.10 coins with her are?
Please give answer in full process.

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Total\:no.\:of\:5\:rupees\:coin=18}}}$

$\green{\tt{\therefore{Total\:no.\:of\:10\:rupees\:coin=7}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Total \: no. \: of \: coins = 25 \\ \\ \tt: \implies Total \: amount = 160 \: rupees \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Total \: no. \: of \: 5 \: rupees \:coin =? \\ \\ \tt: \implies Total \: no. \: of \: 10 \: rupees \:coin =?$

• According to given question :

$\tt \circ \: Let \: total \: no. \: of \: 5 \: rupees \: coin \: be \: x \\ \\ \tt \circ \: Let \: total \: no. \: of \: 10\: rupees \: coin \: be \: y\\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies x + y = 25 \\ \\ \tt: \implies x = 25 - y - - - - - (1) \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies 5x + 10y = 160 \\ \\ \tt: \implies x + 2y = 32 \\ \\ \tt: \implies 25 - y + 2y = 32 \\ \\ \tt: \implies y = 32 - 25 \\ \\ \green{\tt: \implies y = 7 \: coins} \\ \\ \text{Putting \: value \: of \: y \: in \: (1)} \\ \tt: \implies x = 25 - 7 \\ \\ \green{\tt: \implies x = 18 \: coins}\\ \\ \green{\tt \therefore Total \: no. \: of \: 5 \: rupees \: coin \: is \: 18} \\ \\ \green{\tt \therefore Total \: no. \: of \: 10\: rupees \: coin \: is \: 7}$

Answer 2

$\huge\sf\pink{Answer}$

☞ Number of 10 Rupee coins = 7

☞ Number of 5 Rupee coins = 18

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ Ayesha has Rs 5 and Rs 10 coins.

✭ She has a total of 25 coins

✭ Sum of money she has = Rs 160

$\rule{110}1$

$\huge\sf\gray{To\:Find}$

☆ The number of 5 and 10 Rupee coin she have?

$\rule{110}1$

$\huge\sf\purple{Steps}$

❍ Let the number of 10 Rupee coins she have be x

❍ Let the number of 5 Rupee coins she have be y

➝ $\sf x + y = 25$

➝ $\sf x = 25-y \qquad \frac{\quad}{}eq(1)$

Also,

$\sf\longmapsto 10x+5y = 160$

$\sf\longmapsto 5(2x+y)= 160$

$\sf\longmapsto 2x+y = 32$

$\sf\longmapsto y = 32 - 2x$

Substituting the value of x[eq(1)]

$\sf\dashrightarrow y = 32 - 2(25-y)$

$\sf\dashrightarrow y = 32 - 50 +2y$

$\sf\dashrightarrow y - 2y = 33-50$

$\sf\dashrightarrow -y = -18 \qquad\bigg\lgroup - gets \ cancelled \bigg\rgroup$

$\sf\color{lime}{\dashrightarrow y = 18}$

Substituting the value of y in eq(1)

$\sf\leadsto x = 25 - 18$

$\sf\color{aqua}{\leadsto x = 7}$

$\rule{170}3$