Question

The ratio of oblong tables to round tables at a conference is 3:5. The total number of tables at the conference is 72. How many of each type are there? There are ? Oblong tables and ? Round tables. Solve for both question marks.

Answer 1

To solve this problem, set up a system of equations to represent the given information. The number of oblong tables is 27 and the number of round tables is 45.

Step-by-step explanation:

To solve this problem, we can set up a system of equations to represent the given information. Let's use 'o' to represent the number of oblong tables and 'r' to represent the number of round tables.

We know that the ratio of oblong tables to round tables is 3:5, so we can write the equation:

o/r = 3/5

Since the total number of tables is 72, we can also write the equation:

o + r = 72

To solve this system of equations, we can use substitution or elimination method. Let's use substitution:

From the first equation, we can solve for o in terms of r:

o = (3/5)r

Substitute this expression for o in the second equation:

(3/5)r + r = 72

Simplify:

(8/5)r = 72

Multiply both sides by (5/8):

r = 45

Substitute this value for r in the first equation:

o = (3/5) * 45

Simplify:

o = 27

Therefore, there are 27 oblong tables and 45 round tables at the conference.

Answer 2

Since the ratio of the oblong tables to round tables is 3: 5

Since the total number of tables is 72

Let us find the sum of the ratios and equate it by 72

`\begin{gathered} 3x+5x=72 \\ 8x=72 \end{gathered}`

Let us divide both sides by 8 to find the value of x, which is the number of units in each type

`\begin{gathered} (8x)/(8)=(72)/(8) \\ x=9 \end{gathered}`

Now multiply 9 by each term of the ratio to find the number of each type

`\begin{gathered} 3*9=27 \\ 5*9=45 \end{gathered}`

There are 27 oblong tables

There are 45 round tables