Question

A restaurant records the number of customers at breakfast, lunch and dinner during one day. the ratio of customers at breakfast to customers at lunch was 3:2. the ratio of customers at breakfast to customers at dinner was 11:8. the number of customers at lunch was 10 less than the number of customers at dinner. how many customers were recorded at lunch?

Answer 1

To find the number of customers at lunch, set up a system of equations using the given ratios and the information provided. Solve the system algebraically using substitution or elimination to find the number of customers at lunch.

Step-by-step explanation:

The student's question involves solving a problem using ratios and algebra. To determine the number of customers at lunch, we need to set up a system of equations based on the given ratios.

Let the number of customers at breakfast, lunch, and dinner be B, L, and D respectively. According to the ratios given in the question:

• Breakfast to lunch ratio is 3:2, so we can write this as B/L = 3/2, or 2B = 3L.
• Breakfast to dinner ratio is 11:8, so B/D = 11/8, or 8B = 11D.
• The number of customers at lunch is 10 less than at dinner, expressed as L = D - 10.

Now, we can use substitution or elimination to solve the system of equations. From the first equation:

1. 2B = 3L (1)
2. 8B = 11D (2)
3. L = D - 10 (3)

From equation (3), we can substitute L into equation (1) to find B in terms of D. Then we can use B to solve for D in equation (2). Finally, we can substitute D back into equation (3) to find L.

After solving, we find out the number of customers at lunch. Although the exact numerical calculation isn't provided because the data wasn't given, this method will provide the answer.