SYSTEMS OF EQUATIONS

Evelyn, Zoe, and Nora are planning a big party at the Country Buffet restaurant. The restaurant has tables that seat 6 people and booths that can seat 4 people. They counted 38 seating units in total, which can accommodate 188 people. They started a fun challenge to figure out the number of tables, t, and the number of booths, b, at the restaurant. Can you help them solve this challenge?

• 4t=386 b=188

• t+b=38 6t+4b=188

• t+b=188 6t+4b=38

• t+b=38 4t+6b=188

Imagine this, Nora, Avery, and Daniel are playing a game of 'Treasure Hunt'. Nora finds a treasure chest filled with quarters and dimes amounting to $6.80. Avery notices that the number of dimes is 3 times the number of quarters. Can you help Daniel figure out a system of equations to find 'q', the number of quarters, and 'd', the number of dimes, in the treasure chest?

• q=3+d 0.25q+0.10d=6.80

• d=3+q q+d=6.80

• q=3d 0.25q+0.10d=6.80

• q=3d q+d=6.80

Graph to solve the systems of equations y=-2x+4y=x-2 The solution is ( _________ , _________ )

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Aiden, Ethan, and Aria were having a friendly competition to solve a problem using substitution. Suddenly, they noticed an error in one of the steps. Can you help them identify which line contains the error?

• Line A

• Line B

• Line C

• Line D

Our friends Liam, Zoe, and Anika were watching Belinda solve a system of equations. Suddenly, they noticed an error! Can you spot which line contains the mistake?

• Line C

• Line D

• Line A

• Line E

• Line B

Imagine you're in a detective club with Ava, Nora, and Henry. Mrs. Ochoa just handed you a piece of work to investigate. Can you spot where the mystery student might have made a mistake?

• Line D

• Line A

• Line B

• Line C

• Line E

Abigail, Sophia, and Lily are on a treasure hunt. They found a mysterious note with two equations: 3x+2y=8 and 4y=-6x+16. They believe solving these equations will lead them to the treasure. Can you help them figure out if these equations have:

• 1 solution

• no solution

• many solutions

David, Aiden, and Mason planned a fun movie night. They bought 9 tickets in total for $54. Adult tickets were priced at $8 each, while the child tickets were $3.50 each. Can you guess how many adult tickets they bought?

• 2 adult tickets

• 3 adult tickets

• 4 adult tickets

• 5 adult tickets

Two burgers and one hotdog cost $4.82. At the same price, one burger and two hotdogs cost $3.70. How much does a hotdog cost?

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Olivia, a budding chemist, has two acid solutions at her disposal. One is a 25% solution and the other is a 50% solution. She needs to create a 200ml solution with 35% acid concentration for her science project. How much of each solution should she use?

• 80ml of the 50% solution and 120ml of the 25% solution

• 150ml of the 50% solution and 50ml of the 25% solution

• 60ml of the 50% solution and 140ml of the 25% solution

• 50ml of the 50% solution and 150ml of the 25% solution