Question 1129051
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Let x be the cost of a hot dog and y be the cost of a hamburger.  Then the given information says<br>
{{{7x+4y = 16.00}}}
{{{4x+7y = 19.75}}}<br>
Typically, you would solve the pair of equations using elimination, to find the values of x and y.<br>
But observe that the question does NOT ask you to find the cost of each hot dog and each hamburger; it only asks you to find the cost of one of each.<br>
And a quick look at the equations for the problem should show a quick way to the answer: adding the two equations gives the cost of 11 hot dogs and 11 hamburgers; then dividing by 11 gives the cost of one of each.  So<br>
{{{11x+11y = 35.75}}}
{{{x+y = 3.25}}}<br>
ANSWER: The cost of one hot dog and one hamburger is $3.25.