Question 927444
Let A = Cost of hot dogs.
Let B = Cost of potato chips
Let C = Cost of a soft drink
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Equation 1:{{{5A + 2B + 4C = 16.5}}} Customers order
Equation 2:{{{A - 2 = B}}} A hotdog is $2 more than a bag of chips
Equation 3: {{{C = 2A - 4.25}}} A soft drink is $4.25 less than 2 hot dogs
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Notice that all three equations contain an "A" variable.
I wrote the equations so that they were already written in terms of A.
Now plug (A-2) into equation 1 for B. Also use (2A - 4.25) for C
Equation 1:{{{5A + 2B + 4C = 16.5}}}
{{{5A + 2*(A-2) + 4*(2A - 4.25) = 16.5}}}
Simplify the equation
{{{5A + 2A - 4 + 8A - 17 = 16.5}}}
Combine like terms
{{{15A - 21 = 16.5}}}
Add 21 to both sides
{{{15A = 37.5}}}
Divides both sides by 15
{{{highlight(A = 2.5)}}}
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Now plug 2.5 into equations 2 & 3 for "A" and solve.
Equation 2:{{{A - 2 = B}}}
{{{(2.5) - 2 = B}}}
{{{highlight_green(0.5 = B)}}}
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Equation 3: {{{C = 2A - 4.25}}}
{{{C = 2*(2.5) - 4.25}}}
{{{C = 5 - 4.25}}}
{{{highlight(C = 0.75)}}}