Question
37 An ice cream shop sells small and large sundaes. One day, 30 small sundaes and 50 large sundaes
were sold for
tax is included in all prices.
If
represent this situation.
Peyton thinks that small sundaes cost
Justify your answer.
Using your equations, determine algebraically the cost of one small sundae and the cost of one
large sundae.
were sold for
tax is included in all prices.
If
represent this situation.
Peyton thinks that small sundaes cost
Justify your answer.
Using your equations, determine algebraically the cost of one small sundae and the cost of one
large sundae.
Ask by Rojas Hobbs. in the United States
Mar 16,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The system of equations is:
Solving these equations, the cost of one small sundae is $4 and one large sundae is $6. Peyton is correct.
Solution
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Beyond the Answer
To represent the situation with a system of equations, we can set up the following based on the sales of small (
-
(From the first day’s sales) -
(From the second day’s sales)
Now, let’s check if Peyton’s prices (
Now for the second equation:
So, while Peyton got one equation correct, he is not consistent across both days’ sales.
To determine the actual costs algebraically, we can solve the system of equations. From the first equation, simplify:
-
(by dividing the first equation by 5) -
(by dividing the second equation by 5)
Now, we can use the elimination or substitution method. Multiplying the first simplified equation by 3 gives:
Now, multiplying the second equation by 2 gives:
Next, we can subtract the two equations:
This simplifies to:
Plugging this back into the first simplified equation gives:
So,
Thus, the cost of one small sundae is
