Question

Answer this question

Answer 1

a = number of "X" sold by shop A

b = number of "Y" sold by shop B

so we know the prices are 1099 and 1299, well, we also know that they both sold the same amount, hmmm we know that shop A sold 8 of the "X" and it also sold "a" of the "Y", hmmm they really sold 8 + a laptops total.

now, we know that shop B sold 14 of the "Y" and it also sold "b" of the "X" model, so they really sold in total 14 + b laptops that month, and we know those two amounts are the same, so we can say that 8 + a = 14 + b.

so since the prices are what they're, we can say that shop B sold in dollars 1099b + 14(1299), and we also know that shop A sold 400 less than that, that is 1099b + 14(1299) - 400.

`8+a=b+14\implies \boxed{a=b+6} \\\\[-0.35em] ~\dotfill\\\\ \underset{\textit{total \$ sold by A}}{\stackrel{X}{8(1099)}+\stackrel{Y}{1299a}}~~ = ~~\underset{\textit{total \$ sold by B minus 400}}{( ~~ \stackrel{X}{1099b}+\stackrel{Y}{14(1299)} ~~ ) - 400} \\\\\\ \stackrel{\textit{substituting from the 1st equation}}{8(1099)+1299(b+6)}~~ = ~~1099b+14(1299)-400 \\\\\\ 8(1099)+1299b+6(1299)~~ = ~~1099b+14(1299)-400 \\\\\\ 8(1099)+200b+6(1299) =14(1299)-400`

`200b =14(1299)-400-8(1099)-6(1299) \\\\\\ b=\cfrac{14(1299)-400-8(1099)-6(1299)}{200}\implies \stackrel{\textit{brand X sold by shop B}}{b=6} \\\\\\ \underset{\textit{total money collected by shop B}}{\stackrel{X}{1099b}+\stackrel{Y}{14(1299)}}\implies 1099(6)+14(1299)\implies \stackrel{\textit{collected by shop B}}{24780}`