Question

a furniture factory makes 5 recliners for evert 2 couches. if the factory makes a total of 154 recliners and couches n a dat how many recliners were made

Answer 1

Let \( r \) represent the number of recliners and \( c \) represent the number of couches. According to the problem:

1. The factory makes 5 recliners for every 2 couches. This can be expressed as the ratio:
\[
\frac{r}{c} = \frac{5}{2}
\]
From this, we can write:
\[
r = \frac{5}{2}c \quad (1)
\]

2. The total production of recliners and couches is 154:
\[
r + c = 154 \quad (2)
\]

Now, we can substitute equation (1) into equation (2):
\[
\frac{5}{2}c + c = 154
\]

To combine the terms, we can express \( c \) as \( \frac{2}{2}c \):
\[
\frac{5}{2}c + \frac{2}{2}c = 154
\]
\[
\frac{7}{2}c = 154
\]

Now, multiply both sides by 2 to eliminate the fraction:
\[
7c = 308
\]

Now, divide by 7:
\[
c = \frac{308}{7} = 44
\]

Now that we have the number of couches, we can substitute back to find \( r \):
\[
r = \frac{5}{2}c = \frac{5}{2} \times 44 = 5 \times 22 = 110
\]

Thus, the number of recliners made is:
\[
\boxed{110}
\]