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A restaurant has a total of 48 tables. There are three types of tables. Each small table seats 2
people. Each medium-sized table seats 5 people and each large table seats 12 people. A total
of 235 customers are seated when all the seats are taken up. There are 7 large tables. How
many medium-sized tables are there?
assumption method
7×12 = 84
235-84 = 151
48-7 = 41
assume all 41 tables r small
41×2 = 82
151-82 = 69
each → M-S = 5-2 = 3
69÷3 = 23 (Ans)
number of small tables --- x
number of large tables = 7
number of medium tables = 41-x
(check: x + 7 + 41-x = 48)
2x + 5(41-x) + 12*7 = 235
2x + 205 - 5x + 84 =235
-3x = -54
x = 18
so 18 small tables,
23 medium tables
7 large tables
To solve this problem, we can use algebraic equations to represent the given information.
Let's say the number of small tables is x, the number of medium-sized tables is y, and the number of large tables is z.
We are given the following information:
1) The total number of tables: x + y + z = 48 (Equation 1)
2) Each small table seats 2 people, so the total number of seats for small tables is 2x.
3) Each medium-sized table seats 5 people, so the total number of seats for medium-sized tables is 5y.
4) Each large table seats 12 people, so the total number of seats for large tables is 12z.
5) The total number of customers seated when all seats are taken up is 235: 2x + 5y + 12z = 235 (Equation 2)
We are also given that there are 7 large tables: z = 7.
Now, we can substitute the value of z in Equation 1 and Equation 2:
x + y + 7 = 48 -> x + y = 48 - 7 -> x + y = 41
2x + 5y + 12(7) = 235 -> 2x + 5y + 84 = 235 -> 2x + 5y = 235 - 84 -> 2x + 5y = 151
Now we have a system of two equations:
x + y = 41 (Equation 3)
2x + 5y = 151 (Equation 4)
We can solve this system of equations to find the values of x and y.
Multiplying Equation 3 by 2:
2(x + y) = 2(41) -> 2x + 2y = 82 (Equation 5)
Subtracting Equation 5 from Equation 4:
(2x + 5y) - (2x + 2y) = 151 - 82
Simplifying and solving for y:
3y = 69 -> y = 69/3 -> y = 23
Therefore, there are 23 medium-sized tables in the restaurant.