At a tennis match the snack bar sells hot dogs for 4 dollars and slices of pizza for 5 dollars. The snack bar sold 49 hot dogs and slices of pizza all together for $221 dollars. Part A: Enter the total number of hot dogs sold. Part B: Enter the total number of slices of pizza sold.
The Correct Answer and Explanation is:
Part A (hot dogs): 24
Part B (pizza slices): 25
Why those numbers work
Whenever you see a problem that gives you two totals—one for quantity (how many items) and one for cost (how much money)—it is almost always solved cleanly by setting up a system of two linear equations. Think of the two unknowns we need:
- hh = number of hot dogs sold
- pp = number of pizza slices sold
1. Build the “how many” equation
The statement “sold 49 hot dogs and slices of pizza altogether” tells us the combined count is 49. In symbols: h+p=49.h + p = 49.
This captures the physical total—literally how many individual items left the snack bar.
2. Build the “how much money” equation
Each hot dog brings in $4; each pizza slice brings in $5. Multiplying the price by the quantity of each item and then adding gives the total revenue of $221: 4h+5p=221.4h + 5p = 221.
3. Solve the system
There are many ways—substitution, elimination, or matrices. Substitution is quick here.
From the first equation: p=49−h.p = 49 – h.
Plug that expression for pp into the money equation: 4h+5(49−h)=221.4h + 5(49 – h) = 221.
Distribute and combine like terms: 4h+245−5h=221⇒−h+245=221⇒−h=−24⇒h=24.4h + 245 – 5h = 221 \Rightarrow -h + 245 = 221 \Rightarrow -h = -24 \Rightarrow h = 24.
So 24 hot dogs were sold.
Use hh to find pp: p=49−h=49−24=25.p = 49 – h = 49 – 24 = 25.
So 25 pizza slices were sold.
4. Reasonableness check
- Quantities are whole numbers (makes sense for individual items).
- Prices are realistic multiples: 24×$4=$9624 \times \$4 = \$96 and 25×$5=$12525 \times \$5 = \$125.
- Adding the money confirms the total: $96 + $125 = $221.
- Adding the items confirms the count: 24 + 25 = 49.
Both checks pass, so the numbers are consistent with every fact given in the problem.
