Question: At a baseball game, a vendor sold a combined total of 242 sodas and hot dogs. The number of sodas…

At a baseball game, a vendor sold a combined total of 242 sodas and hot dogs. The number of sodas sold was 48 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.

Number of sodas sold:

Number of hot dogs sold:

Solution

At a baseball game, a vendor sold a combined total of 242 sodas and hot dogs. The number of sodas sold was 48 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold. Let \( s \) be the number of sodas sold and \( h \) be the number of hot dogs sold. Write the equations based on the problem description: \[ \begin{cases} s + h = 242 & \\ s = h + 48 & \end{cases} \] Substitute the second equation into the first equation: \[ (h + 48) + h = 242 \] Simplify and solve for \( h \): \[ 2h + 48 = 242 \] Subtract 48 from both sides: \[ 2h = 194 \] Divide both sides by 2: \[ h = 97 \] Substitute \( h = 97 \) back into the second equation to find \( s \): \[ s = 97 + 48 \] Simplify: \[ s = 145 \] So, the number of sodas sold is 145 and the number of hot dogs sold is 97.