Question

1.

An unknown number y is 15 more than an unknown number x. The number y is also x less than 8. The equations to find x and y are shown below.

y = x + 15
y = –x + 8

Which of the following statements is a correct step to find x and y? (4 points)



Multiply the equations to eliminate y.
Add the equations to eliminate x.
Write the points where the graphs of the equations intersect the x-axis.
Write the points where the graphs of the equations intersect the y-axis.
2.
Variable a is 4 more than variable b. Variable a is also 1 less than b. Which of the following pairs of equations best models the relationship between a and b? (4 points)



a = b + 4
a = b – 1
a = 4b
a = b + 1
b = a + 4
b = a – 1
b = 4a
b = a + 1
3.
Betsey is 11 years older than Waldo. Betsey's age is 15 years less than three times Waldo's age. The system below models the relationship between Betsey's age (b) and Waldo's age (w):

b = w + 11
b = 3w – 15

Which of the following methods is correct to find Betsey's and Waldo's age? (4 points)



Solve w + 11 = 3w – 15 to find the value of w.
Solve b + 11 = 3b – 15 to find the value of b.
Write the points where the graphs of the equations intersect the x-axis.
Write the points where the graphs of the equations intersect the y-axis.
4.
A matinee ticket costs $6 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who saw a movie was 35, and the total money collected was $70. Which of the following options represents the number of children and the number of adults who saw a movie that day, and the pair of equations that can be solved to find the numbers? (4 points)



7 children and 28 adults
Equation 1: a + c = 35
Equation 2: 6a – c = 70
7 children and 28 adults
Equation 1: a + c = 35
Equation 2: 6a + c = 70
28 children and 7 adults
Equation 1: a + c = 35
Equation 2: 6a + c = 70
28 children and 7 adults
Equation 1: a + c = 35
Equation 2: 6a – c = 70
5.
Bella and Heather put some money into their money boxes every week. The amount of money (y), in dollars, in their money boxes after a certain amount of time (x), in weeks, is shown by the equations below:

Bella: y = 25x + 60
Heather: y = 30x + 10

After how many weeks will Bella and Heather have the same amount of money in their money boxes, and what is that amount? (4 points)



10 weeks, $10
10 weeks, $310
9 weeks, $310
310 weeks, $10

Answer 1

1. Add the equations to eliminate x. You already have x and -x so it would be easy to cancel them out.

2. a=b+4 and a=b-1. If a is four more than b, a must equal b+4. If a is one less than b, it must equal b-1.

3. Option A. Because the two both define variable b, they are equivalent.

4. 6a+c=70 and a+c=35. There should be 8 adults and 28 children since 8+27=35 and 6(8)+1(28)= 70

5. 25x+60=30x+10
60=5x+10
50=5x
10=x

y=25(10)+60
y=250+60
y=310

Final answer: 10 wks, $310

Answer 2

1. add the 2 equations, since you have x and -x the x would be removed giving you y

2. a is 4 more than b = a = b+4

a is 1 less than b = a=b-1

so the first pair is correct.

3. Solve w + 11 = 3w – 15 to find the value of w, then you can use the value of w to find b

4. 3rd answer:

28 children and 7 adults
Equation 1: a + c = 35 ( 28+7 = 35)
Equation 2: 6a + c = 70 (6*7=42, 42+28 = 70)

5. 25x+60 = 30x+10

50 = 5x

x = 50/5 = 10 weeks

25(10) = 250+60 = 310 dollars

2nd answer 10 weeks, $310