To determine how many yards Johnnie needs to mow to ensure he does not earn more than $900, we can set up an inequality. Let \( x \) represent the number of yards he mows. The total amount Johnnie earns is given by the expression \( 7x \).
The inequality can be expressed as:
\[ 7x \leq 900 \]
Now, let's solve the inequality for \( x \):
\[ x \leq \frac{900}{7} \] \[ x \leq 128.57 \]
Since Johnnie can't mow a fraction of a yard, we round down to the nearest whole number:
\[ x \leq 128 \]
Therefore, Johnnie can mow a maximum of 128 yards to ensure he does not exceed $900.
Now, we can create a table with three columns: the number of yards mowed (x), the amount earned ($), and the total balance in John's account after mowing.
| Yards Mowed (x) | Amount Earned ($) | Total Balance ($) | |------------------|-------------------|-------------------| | 0 | 0 | 0 | | 10 | 70 | 70 | | 20 | 140 | 140 | | 30 | 210 | 210 | | 40 | 280 | 280 | | 50 | 350 | 350 | | 60 | 420 | 420 | | 70 | 490 | 490 | | 80 | 560 | 560 | | 90 | 630 | 630 | | 100 | 700 | 700 | | 110 | 770 | 770 | | 120 | 840 | 840 | | 128 | 896 | 896 |
In this table, you can see that as Johnnie mows more yards, his earnings increase as well. He can mow up to 128 yards without exceeding his target of $900.
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