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The lawton family spent a total of 26.75 on lunch. They bought 5 drinks and 3 sandwiches. Each drink costs $2.50 less than a sandwich. How do you find the cost of each sandwich?

1 Answer

Oct 27, 2016

The result makes no sense in the real world but according to the supplied values a sandwich costs $$ 4.90 58$ $$4.90 58$
(Possibly the total bill should have been $ $26.70$ $26.70$ (???))

Explanation:

Let
$XXX d$ $color(white)("XXX")d$ represent the cost of a drink, and
$XXX s$ $color(white)("XXX")s$ represent the cost of a sandwich.

We are told
[1] $XXX 5 d + 3 s = 26.75$ $color(white)("XXX")5d+3s=26.75$
and
[1] $XXX d = s - 2.50$ $color(white)("XXX")d=s-2.50$

Using [2] we can replace $d$ $d$ with $(s - 2.50)$ $(s-2.50)$ in [1] to get
$XXX 5 (s - 2.50) + 3 s = 26.75$ $color(white)("XXX")5(s-2.50)+3s=26.75$

Simplifying
$XXX 5 s - 12.50 + 3 s = 26.75$ $color(white)("XXX")5s-12.50+3s=26.75$

$XXX 8 s = 39.25$ $color(white)("XXX")8s= 39.25$

$XXX s = 4.90 \frac{5}{8}$ $color(white)("XXX")s=4.90 5/8$

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