Question 394960

let {{{x = cars}}} and {{{y = trucks}}}


since there were {{{32_ vehicles}}}, we have {{{ x + y = 32}}}


cars have {{{4 _wheels}}} so {{{4x}}}, trucks have {{{6_ wheels}}} so {{{6x}}}


 the {{{total}}}{{{ number}}} of wheels is {{{148}}}, so


{{{4x + 6y = 148}}}


set up an equation system and solve it:


{{{x + y = 32}}}


{{{4x + 6y = 148}}}


multiply the top equation by {{{-4}}} to get rid of {{{x}}} and solve for {{{y}}}:

{{{-4x - 4y = - 128}}}


{{{4x + 6y = 148}}}
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{{{2y = 20}}}


{{{y = 10}}}


so {{{10}}} trucks and {{{22}}} cars were involved


check: {{{4(22) + 10(6) = 88 + 60 = 148}}}