1. The sum of two numbers is 15 and their difference is 3. If a system of equations is graphed for this scenario, the intersection point gives the two numbers. The larger number is ___.
2. A rectangle has a perimeter of 30 cm. Its length is twice its width. Which system of equations represents this situation, where $L$ is the length and $W$ is the width?
3. A school sold 100 tickets for a concert. Adult tickets cost 10 dollars and child tickets cost 6 dollars, raising 760 dollars. The intersection of the graphed system is $(a, c)$. What is the value of $a$? $a$ = ___.
4. When solving a real-world problem by graphing a system of two linear equations, what is the significance of the point where the two lines intersect?
5. One number is 5 more than another. The sum of the two numbers is 21. If this problem is modeled by a system of equations, the solution reveals the two numbers. The smaller number is ___.
6. A school store sold 80 items, a mix of notebooks ($n$) at $3$ each and pens ($p$) at $2$ each. The total sales were $210. Which system of equations models this situation?
7. The sum of two numbers is 45. The larger number is 9 more than the smaller number. What is the value of the smaller number? ___
8. A jar contains 35 coins, consisting of only nickels ($n$) and dimes ($d$). The total value of the coins is $2.50. How many dimes are in the jar? ___
9. The perimeter of a rectangular garden is 80 feet. The length ($l$) is 5 feet less than three times its width ($w$). Which system of equations describes the garden's dimensions?
10. At a farm, there are 50 animals, all of which are either chickens (2 legs) or pigs (4 legs). If there is a total of 140 legs, how many pigs are on the farm? ___