Question 1206418
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The number of ties he bought is 2/3 the number of shirts, so...<br>
Let 3x = # of shirts
then 2x = # of ties<br>
Let y = price of each shirt
then y+14 = price of each tie<br>
The total cost was $2385:
{{{(3x)(y)+(2x)(y+14)=2385}}}
{{{5xy+28x=2385}}} [1]<br>
The ties cost $127.80 more than the shirts:
{{{(2x)(y+14)-(3x)(y)=127.8}}}
{{{-xy+28x=127.8}}} [2]<br>
Multiply [2] by 5 and add to [1] to eliminate the xy terms to solve for x<br>
{{{-5xy+140x=639}}}
{{{168x=3024}}}
{{{x=3024/168=18}}}<br>
The number of shirts was 3x = 54
The number of ties was 2x = 36<br>
Substitute x=18 in [1] to solve for y<br>
{{{90y+504=2385}}}
{{{90y=1881}}}
{{{y=1881/90=20.9}}}<br>
The price of each shirt was y = $20.90
The price of each tie was y+14 = $34.90<br>
ANSWERS:
(a) total cost of the shirts: 54($20.90) = $1128.60
(b) number of ties: 36<br>