120𝑥 + 14,000 ≤ 20,000
Let x be the number of new shoes the team can purchase. Therefore, the team can purchase 120𝑥120x.
The team had $20,000 and spent $14000. Now the team can spend on new shoes $6000 at most.
Now, write the inequality:
120𝑥+14,000≤20,000
The ratio of boys to girls is 4:7.
Therefore, there are 4 boys out of 11 students.
First, divide the total number of students by 11, then multiply the result by 4.
44÷11=4⇒4×4=16
There are 16 boys and 28(44–16) girls. So, 12 more boys should be enrolled to make the ratio 1:1
The width of the rectangle is twice its length. Let 𝑥 be the length. Then, width =2𝑥
Perimeter of the rectangle is (2 (width + length) =2(2𝑥+𝑥)=60⇒6𝑥=60⇒𝑥=10
The length of the rectangle is 10 meters.
The equation of a line in slope intercept form is: 𝑦=𝑚𝑥+𝑏y
Solve for y.
4𝑥−2𝑦=12⇒−2𝑦 = 12−4𝑥⇒𝑦=(12−4𝑥)÷(−2)⇒𝑦=2𝑥−6
The slope of this line is 2.
The product of the slopes of two perpendicular lines is −1.
Therefore, the slope of a line that is perpendicular to this line is:
𝑚1×𝑚2=−1⇒2×𝑚2=−1⇒𝑚2=−1/2
Solving Systems of Equations by Elimination
Multiply the first equation by (-2), then add it to the second equation.
−2(2𝑥+5𝑦=11) 4𝑥−2𝑦=−14⇒−4𝑥−10𝑦=−22 4𝑥−2𝑦=−14⇒−12𝑦=−36⇒𝑦=3
Plug in the value of y into one of the equations and solve for x.
2𝑥+5(3) = 11⇒2𝑥+15 = 11⇒2𝑥 = −4⇒𝑥= −2
Answer : 8
Use formula of rectangle prism volume.
𝑉=(𝑙𝑒𝑛𝑔𝑡ℎ)(𝑤𝑖𝑑𝑡ℎ)(ℎ𝑒𝑖𝑔ℎ𝑡)⇒2000 = (25)(10)(ℎ𝑒𝑖𝑔ℎ𝑡)⇒ℎ𝑒𝑖𝑔ℎ𝑡 = 2000÷250 = 8
This response represents the correct solution to the word problem.
The student may have set up and solved the inequality as shown below, where x represents the number of games played:
4x + 5.25 < 25
4x < 19.75
X < 4.9375
The student who selects this response understands that the greatest number of games played has to be a
whole number less than 4.9375.
This response represents the correct equivalent expression.
(6x - 5 ) - (3x - 2) =
7x - 3z - 5 - ( - 2) =
4x - 3
This response represents the correct percent increase in the number of games the Cougar team won from last year to this year.
20/16 = 125/100
125 - 100 = 25
Plug in the value of x and y.
𝑥=3 and 𝑦=−2
(5(𝑥−2𝑦)+(2−𝑥))2 = (5(3−2(−2))+(2−3))2 = (5(3+4)+(−1))2 =(34)2 = 36
Use PEMDAS (order of operation):
[6×(−24)+8]– (−4) + [4×5]÷2
[−144+8]– (−4) + [20]÷2= [−144+8]– (−4)+10
[−136]– (−4) + 10=10 [−136] + 4+10 = 14 –122
This response represents the correct total amount Angela paid. The student may have used the following representations to solve the problem:
X = 2.75 + 3(2.5) /2 + 1./75
X = 2.65 + 3.65 + 1.75
X = 8/25
Answer : 729
(36)=3×3×3×3×3×3=729
This response represents the correct expression that shows the expected population in the following year. A student who selects this response understands how the quantities in the expression are related in this problem context.
We can solve this problem using the concept average. That is, the average of 6 tests is 92. Let "x" be the score of 6th test (88 + 91 + 99 + 86 + 92 + x)/6 = 92 (456 + x)/6 = 92 Multiply by 6 on both sides 456 + x = 92 (6) 456 + x = 552 Subtract by 456 on both sides 456 + x - 456 = 552 - 456 x = 96 Hence option (96) is correct.
The population is increased by 15% and 20%.
15% increase changes the population to 115% of original population.
For the second increase, multiply the result by 120%.
(1.15)×(1.20)=1.38=138%
38 percent of the population is increased after two years.
To find the discount, multiply the number by (100%–rate of discount).
Therefore, for the first discount we get: (200)(100%–15%)=(200)(0.85)=170
For the next 15% discount: (200)(0.85)(0.85)
𝑥+2𝑦=4. Plug in the values of 𝑥 and 𝑦 from choices provided. Then:
A. (−3,4)𝑥+2𝑦=4(→)−3+2(4)=4(→)−3+8=4 (This is NOT true!)
B. (−2,3)𝑥+2𝑦=4(→)−2+2(3)=4(→)−2+6=4 This is true!
C. (1,2)𝑥+2𝑦=4(→)1+2(2)=4(→)1+4=4 (This is NOT true!)
D. (−1,3)𝑥+2𝑦=4(→)−1+2(3)=4(→)−1+6=4 (This is NOT true!)
Kate drove 180 miles at 60 mph to reach the meeting place where Rose arrived after driving 240 miles at 80 mph.
In the stadium the ratio of home fans to visiting fans in a crowd is 5:75:7. Therefore, total number of fans must be divisible by 12:5+7=12.12:5+7=12.
Let’s review the choices:
A. 42,326:42,326÷12=3,527.16642,326:42,326÷12=3,527.166
B. 66,812:66,812÷12=5,567.66666,812:66,812÷12=5,567.666
C. 12,324:12,324÷12=102712,324:12,324÷12=1027
D. 44,566:44,566÷12=3,713.83344,566:44,566÷12=3,713.833
Only choice A when divided by 12 results a whole number.
The sum of supplement angles is 180.
Let 𝑥x be that angle. Therefore, 𝑥+5𝑥=180x+5x=180 6𝑥=1806x=180,
divide both sides by 6: 𝑥=30
The area of the floor is: 6 cm × 24 cm = 144 cm²
The number of tiles needed =144÷8=18
Let "x" be his uncle's present age
5 years ago, his uncle's age = x - 5
5 years ago, Noel's age = 14 - 5 = 9
(x - 5)/3 = 9
Multiply by 3 on both sides
x - 5 = 9 (3)
x - 5 = 27
Add 5 on both sides
x - 5 + 5 = 27 + 5
x = 32
Hence option (32) is correct.
14x - 7y - 4 = 45
Subtract 14x and add 4 on both sides
14x - 7y - 4 - 14x + 4 = 45 - 14x + 4
-7y = 45 - 14x + 4
-7y = 49 - 14x
Divide by -7 into both sides
-7y/(-7) = (49 - 14x)/(-7)
y = (14x - 49)/7
y = (14x/7) - (49/7)
y = 2x - 7
Here PX is the radius of the first circle, QX is the radius of the second circle. PQ is the distance between two centers.
PX = PQ = QX
Hence the required angle is 60°.
Jack has d dollars.
Neil has 3d dollars
Number of dollars that Sean has = (1/2)(d + 3d) - 80
= (1/2) 4d - 80
= 2d - 80
Hence the answer is 2d - 80.
Since the numerator and denominator are the same, we always get the value 1 for f(x).
So, the answer is infinitely many.
This response represents the correct cost of each pants, $35, which results from solving the equation 4x + 20 = 160.
The student who selects this response understands how to solve the given word problem.
4x + 20 = 150
4x = 140
X = 35
4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16
Prime numbers are 5, 7, 11, 13
Hence there are 4 prime numbers between 4 and 16.
Number of students in the class = 28
Number of boys = (2/(2+5)) ⋅ 28
= (2/7) ⋅ 28
= 2(4)
= 8
Number of girls = 5/(2+5) ⋅ 28
= (5/7) ⋅ 28
= 5(4)
= 20
(8 + y) : (20 + y) = 1 : 2
(8 + y) / (20 + y) = 1/2
2(8 + y) = 1 (20 + y)
16 + 2y = 20
2y = 20 - 16
2y = 4
y = 2
Hence the number of students to be added is 2.
