Word Problems - Systems of Equations (A)

Kristy is starting up a home baking company. She sold one customer 12 cookies and 12 cupcakes for $126. She sold another customer 20 cookies and 30 cupcakes for $270. What is the price of a cookie and the price of a cupcake?

An equation to represent the blue sentence is: ​ (a)  

An equation to represent the red sentence is: ​ ​ (b)  

• 12x + 12y = 126
• 20x + 30y = 270
• x + y = 126
• 12x + 30y = 270
• 24x + 126 = 270

Julie is counting the amount of protein in her food. If Julie eats 5 eggs and 1 yogurt cup, then she will eat 47 grams of protein. If Julie eats 2 eggs and 2 yogurt cups, then she will eat 38 grams of protein. How many grams of protein are in an egg and a protein cup?

An equation to represent the blue sentence is: ​ (a)  

An equation to represent the red sentence is: ​ ​ (b)  

• 5x + 1y = 47
• y = 47 + 5x
• 5x + 38 = 47
• y = 47x + 38
• 2x + 2y = 38

Mary is buying boxes of crayons and glue sticks for daycare. Mary purchases a total of 28 items. Each box of crayons costs $1 apiece, and each glue stick costs $0.50 apiece, and Mary spent a total of $19. How many boxes of crayons and how many glue sticks did Mary purchase?

An equation to represent the blue sentence is: ​ (a)  

An equation to represent the red sentence is: ​ ​ ​ (b)  

• x + y = 28
• x + y =19
• 28x + 1.50y = 19
• y = 28 + 19y
• 1x + 0.50y = 19

Carol is considering which season pass to get to her favorite amusement park. A gold tier season pass costs $110 and she is able to get soda refills for $3 each. A platinum tier season pass costs $130 and she is able to get soda refills for $1 each. After how many sodas will the two plans cost the same?

An equation to represent the blue sentence is: ​ ​ (a)  

An equation to represent the red sentence is: ​ ​ ​ (b)  

• x + 3y = 110
• x + y = 130
• 130x + 110y = 3
• y = 130 + 1x
• y = 110 + 3x

There are Sprites & Gatorade's in a cooler. There are a total of 30 drinks in the cooler. The amount of Gatorade's is double the amount of Sprites. How many Sprites and how many Gatorade's are in the cooler?

An equation to represent the blue sentence is: ​ ​ ​ (a)  

An equation to represent the red sentence is: ​ ​ ​ (b)  

• 2x + y = 30
• 30x + 2 = y
• x + 30 = 2y
• y = 2x
• x + y = 30