Question

3 hats and 2 scarves costs £12 5 hats and 4 scarves costs £21

Answer 1

$Let \: the \: cost \:of \: a \:hat = £x$

$The \:cost\:of \: a \: scarves = £y$

/* According to the problem given */

$3x + 2y = £12 \: --(1)$

$and \: 5x + 4y = £21 \: --(2)$

/* Multiplying equation (1) by 2 , we get */

$\implies 6x + 4y = 24 \: --(3)$

/* Subtract equation (2) from equation (3), we get */

$6x + 4y - (5x + 4y ) = 24 - 21$

$\implies 6x + 4y - 5x - 4y = 3$

$\implies x = 3$

/* Put x = 3 in equation (1), we get */

$\implies 3\times 3 + 2y = 12$

$\implies 9 + 2y = 12$

$\implies 2y = 12 - 9$

$\implies 2y = 3$

$\implies y = \frac{3}{2}$

Therefore.,

$\red{The \: cost \:of \: each \:hat}\green{ = £3}$

$\red{The \: cost \:of \: each \:scarf}\\\green{ = \frac{£3}{2}}$

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