Question

Write a system of equations you could use to solve each problem.

1. Large pizzas are $12 each and small pizzas are $9 each. You spent $150 and bought 2 more large than small pizzas. How many did you buy of each?
2. Santa has 50 more elves than reindeer. He has a total of 350 altogether. How many does he have of each?
3. Mrs. Claus is selling cookies to raise money for presents. She sells chocolate chip cookies for $4 a bag and sugar cookies for $3 a bag. She sold 32 bags of cookies for $108. How many did she sell of each?
4. The sum of 2 numbers is 16. The difference is 6. Find the numbers
5. The sum of the 2 boys’ ages is 35. The difference is 5. Find the 2 numbers.
6. Rudolph’s age is 3 years more than Dasher’s age. The sum of their ages is 77. Find both ages
7. You have $2.90 worth of dimes and quarters. There are 2 more dimes than quarters. How many do you have of each?

Answer 1

A system of equations is established for each problem to determine the quantities or numbers involved, such as the number of pizzas, elves and reindeer, types of cookies, ages, and amounts of coins.

Step-by-step explanation:

To solve each problem posed by the student, we can set up a system of equations to find the quantities or numbers asked for in the questions.

Example Solutions:

1. Let L represent the number of large pizzas and S represent the number of small pizzas. We can establish this system of equations:
   12L + 9S = 150
   L = S + 2
2. Let E represent the number of elves and R represent the number of reindeer. The system would be:
   E = R + 50
   E + R = 350
3. Let C represent the chocolate chip cookie bags and Su represent the sugar cookie bags. The system is:
   4C + 3Su = 108
   C + Su = 32
4. For two numbers x and y where their sum is 16 and their difference is 6, the system is:
   x + y = 16
   x - y = 6
5. If we name the boys' ages A and B, the equations would be:
   A + B = 35
   A - B = 5
6. For Rudolph and Dasher's ages, let R be Rudolph's age and D be Dasher's age. The system is:
   R = D + 3
   R + D = 77
7. With D representing the number of dimes and Q representing the number of quarters, we use:
   10D + 25Q = 290
   D = Q + 2

By solving each system of equations, we can determine the exact quantities or numbers for each scenario.