9. Carlos is saving money to buy a set of golf clubs that cost [tex]$\$[/tex]530[tex]$. He already has $[/tex]\[tex]$80.00$[/tex] saved and can earn the rest of the money by mowing 15 lawns. If [tex]$m$[/tex] represents how much he earns for mowing each lawn, which of the following equations can be solved to find how much Carlos is paid for mowing each lawn?
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:
