Question

1. leo’s lawn mowing service has $300 in start - up expenses, and charges $30 for each yard. yan’s yards does not have any start - up expenses and charges $20 for each yard. after how many yards will the profits of the two businesses be the same?
2. two students collect baseball cards. shushu has 210 cards, and vivak has 160 cards. shushu adds 8 new cards to her collection each month, and vivak adds 13 new cards each month. after how many months will they have the same number of baseball cards?
3. wilson middle school wants to rent tables for their weeklong art festival. one rental company charges a $20 setup fee and $12 per table for the week. another rental company charges a $30 setup fee and $10 per table for the week. how many tables can the school rent for the charge to be the same for both companies?
4. two buses are leaving from different schools to carry students to a band competition. bus a travels 160 miles the first day, and an average of 60 miles per hour on the second day. bus b travels 240 miles the first day of the trip, and an average of 50 miles per hour on the second day. after how many hours on the second day will both buses have driven the same total number of miles?
5. a baseball player averages 2 hits per game. the player already has 18 hits this season. another player has 22 hits so far this season and averages 1 hit per game. after how many games will both players have the same number of hits?

Explanation:

Problem 6

Step1: Define variable & profit equations

Let $y$ = number of yards.
Leo's profit: $30y - 300$
Yan's profit: $20y$

Step2: Set profits equal

$30y - 300 = 20y$

Step3: Isolate $y$ terms

$30y - 20y = 300$
$10y = 300$

Step4: Solve for $y$

$y = \frac{300}{10}$

Step1: Define variable & card equations

Let $m$ = number of months.
Shushu's total: $210 + 8m$
Vivak's total: $160 + 13m$

Step2: Set totals equal

$210 + 8m = 160 + 13m$

Step3: Isolate $m$ terms

$210 - 160 = 13m - 8m$
$50 = 5m$

Step4: Solve for $m$

$m = \frac{50}{5}$

Step1: Define variable & cost equations

Let $t$ = number of tables.
Company 1 cost: $20 + 12t$
Company 2 cost: $30 + 10t$

Step2: Set costs equal

$20 + 12t = 30 + 10t$

Step3: Isolate $t$ terms

$12t - 10t = 30 - 20$
$2t = 10$

Step4: Solve for $t$

$t = \frac{10}{2}$

Answer:

30 yards

---

Problem 7