Writing System of Equations Algebra 1 Writing System of Equations

Systems of Equations Writing Equations STEP 1: Read problem. STEP 2: Identify variables and label them. STEP 3: Re-read problem, writing as you go. STEP 4: Double- check your answer. Does it make sense?

Example #1 Mr. Frankel bought 8 tickets to a puppet show and spent $30. He bought a combination of child tickets for $3 each and adult tickets for $5 each. Which system of equations will determine the number of adult tickets, a, and the number of child tickets, c, he bought? a = number of adult tickets c = number of child tickets Tickets: a + c = 8 Money: 5a + 3c = 30

Example #2 Ms. Rechtin purchased 12 boxes containing a total of 70 golf balls. She bought a combination of small boxes, each containing 3 golf balls, and large boxes, each containing 20 golf balls. Which system of equations will determine the number of small boxes, s, and the number of large boxes, l, she bought? s = number of small golf balls l = number of large golf balls Golf balls: s + l = 12 Boxes: 3s + 20l = 70

Example #3 Sam visits the Cookie Store and spends a total of $6.40. Raisin cookies sell for 30cents each and chocolate chip cookies sell for 25cents each. He buys 3 more raisin cookies than chocolate chip cookies. Which system of equations best represents the situation if C represents the number of chocolate chip cookies and R the number of raisin cookies? C = number of chocolate chip cookies R = number of raisin cookies Money: 0.30R + 0.25C = 6.40 Cookies: R = C + 3

Example #4 Sally buys 12 tickets to the Fun-Time Circus for a total of $58. If adult tickets cost $6.00 each and child tickets cost $2.50 each, which System of equations best represents the situation? A represents the number of adult tickets bought and C the number of children tickets bought. A = number of adult tickets C = number of child tickets Money: 6A + 2.50C = 58 Tickets: A + C = 12

Example # 5 Jason went to the Hamburger Shack twice last week. On the first trip he bought 3 hamburgers and 4 orders of french fries for $7.10. On the second trip he bought only 2 hamburgers and an order of french fries for $3.40. Which system of equations best represents this situation if H represents the cost of each hamburger purchased and F the cost of each order of French fries? H = Cost of a hamburger F = Cost of each order of French fries 3H + 4F = 7.10 2H + F = 3.40

Example # 6 Logan went to the cafeteria twice last week. On Monday he had 2 hot dogs and a carton of milk totaling $2. 85. On Wednesday he had 3 hot dogs and 2 cartons of milk totaling $4.45. Which system of equations best represents the situation if H represents the cost of each hot dog and M represents the cost for each carton of milk? M = cost of a carton of milk H = cost of a hotdog 2H + M = 2.85 3H + 22M = 4.45

EXAMPLE #7 The Delicious Ice Cream Shop sells sundaes for $2.00 and bananas splits for $3.00. On a hot summer day the shop sold 7 more sundaes than banana splits and made $110. Which system of equations could be used to find the number of sundaes, s, and banana splits, b, that the shop sold that day? s = number of sundaes b = number of banana splits 2s + 3b = 110 s = b + 7

EXAMPLE #8 The length of a rectangular pool is twelve feet more than the width. The perimeter of the pool is 120 feet. Which system of equations can be used to find the pool’s length and width? l = length of a rectangle w = width of a rectangle l = w + 12 2l + 2w = 120