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

Question

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

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Aaliyah 2 weeks 2021-11-22T00:33:43+00:00 1 Answer 0 views 0

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    2021-11-22T00:35:40+00:00

     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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