Question 242993
Let {{{h}}} = highway miles driven
Let {{{t}}} = in-town miles driven
given:
(1) {{{h + t = 1800}}} mi
(2) {{{h/40 + t/25 = 51}}} gallons
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Note that (miles)/(miles/gallon) = (miles) x (gallons/mile) = gallons
I have 2 equations and 2 unknowns, so it's solvable
(2) {{{h/40 + t/25 = 51}}}
Multiply both sides by {{{200}}}
(2) {{{5h + 8t = 10200}}}
Now multiply both sides of (1) by {{{5}}}
and subtract (1) from (2)
{{{5h + 8t = 10200}}}
{{{-5h - 5t = -9000}}}
{{{3t = 1200}}}
{{{t = 400}}}
Plug this back into (1)
{{{h + t = 1800}}}
{{{h + 400 = 1800}}}
{{{h = 1400}}}
1400 miles were highway miles
check answer:
(2) {{{h/40 + t/25 = 51}}}
{{{1400/40 + 400/25 = 51}}}
{{{35 + 16 = 51}}}
{{{51 = 51}}}
OK