To determine which equation correctly finds how much Carlos earns per lawn, let's break down the problem step-by-step.
Carlos needs to save \[tex]$530 to buy a set of golf clubs. He already has \$[/tex]80 saved and can earn the remaining money by mowing 15 lawns. We need to find the amount, [tex]\(m\)[/tex], he earns per lawn.
First, let's calculate how much more money Carlos needs to save to reach his goal of \[tex]$530:
Amount still needed = Total cost - Amount already saved
Amount still needed = \$[/tex]530 - \[tex]$80
Amount still needed = \$[/tex]450
Carlos earns money by mowing lawns. If he mows 15 lawns, the amount he needs to earn from each lawn mowed (denoted as [tex]\(m\)[/tex]) can be found by dividing the remaining amount needed by the number of lawns:
[tex]\(m\)[/tex] = Amount still needed / Number of lawns
[tex]\(m\)[/tex] = \[tex]$450 / 15
\(m\) = \$[/tex]30 per lawn
Next, we need to find the equation that correctly represents this situation.
Starting with option (A):
[tex]\(530 = 15m + 80\)[/tex]
If we insert the number we found, we need to verify that the equation balances:
[tex]\(530 = 15 \cdot 30 + 80\)[/tex]
[tex]\(530 = 450 + 80\)[/tex]
[tex]\(530 = 530\)[/tex] (True)
The equation is verified and balances correctly.
Now let's quickly examine the other options to show why they are incorrect:
(B)
[tex]\(530 = 15m - 80\)[/tex]
If we insert [tex]\(m = \$30\)[/tex]:
[tex]\(530 = 15 \cdot 30 - 80\)[/tex]
[tex]\(530 = 450 - 80\)[/tex]
[tex]\(530 = 370\)[/tex] (False)
(C)
[tex]\(530 - m = 80\)[/tex]
If we insert [tex]\(m = \$30\)[/tex]:
[tex]\(530 - 30 = 80\)[/tex]
[tex]\(500 = 80\)[/tex] (False)
(D)
[tex]\(530 + 80 = 15m\)[/tex]
If we insert [tex]\(m = \$30\)[/tex]:
[tex]\(530 + 80 = 15 \cdot 30\)[/tex]
[tex]\(610 = 450\)[/tex] (False)
Only option (A) verifies correctly:
[tex]\(530 = 15m + 80\)[/tex]
Therefore, the correct equation that can be solved to find how much Carlos is paid for mowing each lawn is:
(A) [tex]\(530 = 15m + 80\)[/tex]
