Alg SoE word problems

Ben and Amy are both skiing downhill at the same time. Ben starts out at an elevation of 1200 m and skis down at a rate of 3 meters per second. Amy starts out at an elevation of 1400 m and skis down at a rate of 5 meters per second. What would be the set-up for this systems?

x: seconds

y: elevation (m)

• y = 3x + 1200

  y = 5x + 1400

• y = 3x + 1400

  y = 5x + 1200

• y = -3x + 1200

  y = -5x + 1400

• y = -3x + 1400

  y = -5x + 1200

Tags

CCSS.8.EE.C.8C

If you order 5 burgers and 3 fries, it costs a total of $24. A fries costs $2 less than a burger. What would be the two equations for the system of equations?

b = cost of a burger

f = cost of fries

• 5b + 3f = 24

  f = 2 - b

• b + f = 24

  5b + 3f = 24

• 5b + 3f = 24

  b = 2 + f

• f = b - 2

  5b + 3f = 24

Tags

CCSS.HSA.CED.A.3

Josh works 2 different jobs: walking dogs and walking cats. He makes $5 an hour walking dogs and $8 walking cats. One week, he works a total of 20 hours, and he makes a total of $118. How many hours did he work at each job?

x= hours walking dogs

y = hours walking cats

• x + y = 118

  5x + 8y = 20

• 8x + 5y = 118

  x + y = 20

• 5x + 8y = 118

  x + y = 20

• x = 20 + y

  5x + 8y = 118

Tags

CCSS.8.EE.C.8C

Josh works 2 different jobs: teaching and cutting hair. One week, he worked 4 hours teaching and 8 hours cutting hair and made a total of $200. Another week, he worked 7 hours teaching and 9 hours cutting hair and made $320. How much does he make at each job?

x= $ made per hour teaching

y = $ made per hour cutting hair

• 4x + 8y = 200

  7x + 9y = 320

• 4x + 8y = 320

  7x + 9y = 200

• x + y = 200

  7x + 9y = 320

• 8x + 4y = 200

  7x + 9y = 320

Tags

CCSS.8.EE.C.8C

For a big trip, we rent out 47 hotel rooms. If we rented 8 more large rooms than small rooms, how many rooms did we rent in total?

x= # of small hotel rooms

y = # of large hotel rooms

• 8x + y = 47

  x + y = 8

• x + y = 47

  y = 8 + x

• x + y = 47

  x = y + 8

• x + y = 47

  y = x - 8

• x + y = 47

  y = 8x

Tags

CCSS.HSA.CED.A.3

Josh is thinking of two numbers.  Their sum is -10 and their difference is -2.  Which system of equations represents the situation?

• x - y = -10
  x + y = -2
• x = -2 
  y = 5
• x + y = -2
  x - y = -10
• x + y = -10
  x - y = -2

Tags

CCSS.HSA.CED.A.3

Nancy went to the grocery story.  On Monday she purchased 4 apples and 6 bananas for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?

• 4x + 6y = 3
  13.5x - 13y = 6
• x + y = 4
  x - y = 6
• 4x + 6y = 13
  3x + 7y = 13.5
• 4x - 6y = 13
  3x - 7y = 13.5

Tags

CCSS.8.EE.C.8C

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740
• S + A = 530
  4S + 3A = 1740
• S + A = 1740
  3S + 4A = 530
• S + A = 1740
  4S + 3A = 530

Tags

CCSS.HSA.CED.A.3

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

• x + y = 33
  y = 2x - 3
• x + y = 33
  x = 2y - 3
• x + y = 33
  x = 3 - 2y
• x + y = 3
  x = 33 - 2y

Tags

CCSS.HSA.CED.A.3

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total.

To solve, I graphed:

x + y = 21

6x + 4y = 104

I got an intersection point at (10,11). What does that mean in context of the problem?

• There are 10 adults and 11 children.

• There are 11 adults and 10 children.

• The adults are $10 and the children are $11.

• There are 104 adults and 21 children.

Tags

CCSS.8.EE.C.8C