Question

There's a graph with two line that say (y=500x+4000 company A) and (Company B y=250x+5000) what value of monthly sales do the two companies pay the same income

Answer 1

To find the value of monthly sales where both companies have the same income, we set the two equations equal to each other:

1. \( y = 500x + 4000 \) (Company A)
2. \( y = 250x + 5000 \) (Company B)

Setting them equal to find the point of intersection:

\[
500x + 4000 = 250x + 5000
\]

Now, we solve for \( x \):

1. Subtract \( 250x \) from both sides:

\[
500x - 250x + 4000 = 5000
\]

which simplifies to:

\[
250x + 4000 = 5000
\]

2. Subtract \( 4000 \) from both sides:

\[
250x = 1000
\]

3. Finally, divide by \( 250 \):

\[
x = \frac{1000}{250} = 4
\]

Thus, the value of monthly sales \( x \) where both companies pay the same income is \( 4 \) (which could represent thousands, depending on the context).

To confirm, we can substitute \( x = 4 \) back into both equations to check if they yield the same \( y \):

For Company A:

\[
y = 500(4) + 4000 = 2000 + 4000 = 6000
\]

For Company B:

\[
y = 250(4) + 5000 = 1000 + 5000 = 6000
\]

Both companies will have an income of \( 6000 \) at \( x = 4 \). Thus, the monthly sales value at which both companies have the same income is \( 4 \) (thousands).