Ratios, Proportions, and Percentages
Equations
Slippery Slopes
Word Problems
Angles and Triangles
100
Find the unit rate.
84 miles in 12 days
Unit Rate: ____ mi : ____ day
Answer: Unit Rate: 7 mi : 1 day or 7:1
Explanation:
84/12=x/1
84/12=7/1
100
Solve for c.
c -12 = -4
Answer: c = 8
Explanation:
c -12 = -4 (add 12 to both sides)
c= 8
100
Answer: 13.1 km
Explanation:
P=61.4
61.4=17.6 + 17.6 + 2c (add 17.6 + 17.6)
61.4=35.2 + 2c (subtract 35.2 from both sides)
26.2= 2c (divide both sides by 2)
13.1= c
100
Kylie has 17 red beads, and she has 2 fewer yellow beads than red beads. Kylie also has 2 more green beads than red beads. How many beads does Kylie have in all?
Answer: 51 beads
Explanation:
r= 17
y= r-2 (17-2=15)
g= r+2 (17+2=19)
15+17+19= 51
100
Answer: 112 degrees
Explanation:
y= 180-68
y=112
200
Joseph runs 2/3 of a mile in 8 minutes. If Joseph runs at that speed, how long will it take him to run one mile?
Answer: 12 minutes
Explanation:
2/3=8 minutes
1/3= 4 minutes
One mile= 3/3
1/3 + 1/3 + 1/3= 3/3
4 + 4 + 4= 12
200
Solve for z
-2z/3 = 6
Answer: z= -9
Explanation:
-2z/3=6 (multiply both sides by 3)
-2z=18 (Divide both sides by -2)
z= -9
200
Find the slope of the line that passes through (2, 12) and (9, 10).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer: -2/7
Explanation:
Plug (2, 12) and (9, 10) into the slope formula.
200
While on vacation in Chicago, Lara went out for a dinner that cost $75. If sales tax in Chicago is 8% and Lara left a 20% tip on $75, what was the total cost of her meal?
Answer: $96.00
Explanation:
75x .08= tax ($6.00)
75 x .20= tip ($15.00)
75 + 6 + 15 = $96
200
Find the sum of the interior angle measures. Use the formula S=(n-2) x 180. S being the number of sides
Answer: 540 degrees
Explanation:
S=(n-2) x 180
S= (5-2) x 180
S= 3 x 180
S= 540
300
Solve the proportion. Find the value of x.
x/8=7/10
Answer: x = 5.6
Explanation:
x/8=7/10
10x =56
x= 5.6
300
Solve for x.
4x2 = 256
Answer: x= 8 or -8
(only one answer is needed)
Explanation:
4x2 = 256
x2 = 64
x= 8
300
A line has a slope of -10 and includes the points
(–8, z) and (–7,–7). What is the value of z?
Answer: z= 3
Explanation:
300
Jasmine is having friends over to watch a football game. She has 2 1/2 hours until her guests arrive. She spends 2/5 of that time cleaning and the rest of the time preparing snacks.
How much time does Jasmine spend preparing snacks?
Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.
Answer:
1 1/2
Explanation:
Change the mixed number to an improper fraction 2 1/2=5/2
Multiply to find the time spent cleaning (1 hour)
5/2 x 2/5= 10/10 or 1
2 1/2 - 1= 1 1/5 (snacks)
300
A diagram of a triangle is shown. The measure of an interior angle and the measure of an exterior angle are missing. What are the measurments of the two missing angles?
Answer:
Interior Angle: 44 degrees
Exterior Angle: 136 degrees
Explanation:
Interior Angle: 84+52= 136 and 180-136=44 degrees
Exterior Angle: 180-44= 136 degrees
400
Chase is comparing music subscription prices. A 12-month subscription with All Ears costs $91.80 and a 3-month subscription with Press Play costs $19.35.
Which service costs less per month?
Answer: Press Play
Explanation:
Press Play $6.45
$19.35/3=$6.25 and $91.80/12= $7.65
400
Solve for m.
-2m+4m+5= -3
Answer: m= -4
Explanation:
-2m+4m+5= -3 (combine like terms)
-2m + 5= -3 (subtract 5 from both sides)
-2m= -8 (divide both sides by -2)
m= -4
400
A line has a slope of 8 and a y-intercept of -5. Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer: y= 8x-5 or y=8x+ (-5)
Explanation:
y=mx+b
Slope= 8
y-intercept= -5
y= 8x-5 or y=8x+ (-5)
400
Becky is buying fabric to make new pillows for her couch. She spends $71.50 on striped fabric and $52.25 on checkered fabric. If both fabrics cost $5.50 per yard, how many total yards of fabric does she buy?
Write your answer as a whole number or decimal.
Answer: 22.5 yards
Explanation:
$71.50 + $52.25= $123.75 (Total cost)
$123.75 ÷ 5.5 = 22.5
400
The flag is a right triangle with one leg 8 inches long and the other leg 15 inches long. What is the length of the hypotenuse of the triangle in inches?
Answer: 17 inches
Explanation:
a2+b2= c2
82 + 152 = c2
64 + 225 = c2
289 = c2
17 = c
hypotenuse= 17 inches
500
Jonah has a recipe that uses 1 1/2 cups of brown sugar and 2 1/3 cups of flour to make 24 muffins. He has a total of 7 cups of flour. Jonah wants to use all of his flour to make as many muffins as possible using this recipe.
Exactly how many cups of brown sugar will Jonah use if he uses all 7 cups of flour?
Answer: 4 1/2 cups of brown sugar
Explanation:
7 divided by 2 1/3 = 7 x 3/7 = 21/7 = 3 (he can triple the recipe)
1 1/2 x 3 = 3/2 x 3= 9/2 = 4 1/2 cups of brown sugar.
500
Solve for g.
-4(3g-5) + 10g = 19
Answer: g = 1/2 or .5
Explanation:
-4(3g-5) + 10g = 19 (distribute the -4)
-12g + 20 + 10g = 19 (combine like terms)
-2g + 20 = 19 (subtract 20 from both sides
-2g = -1 (divide both sides by -2)
g = .5
500
If y varies directly with x and y= –18 when x=3, find x when y= –12.
Write and solve a direct variation equation to find the answer.
Answer: x=2
Explanation:
y=kx
y= -18 and x= 3
y= -12 and find x
-18=k(3) so k= -6
-12= (-6)x
2=x
500
Gavin is selling water bottles at a baseball game to help raise money for new uniforms. Before the game, he buys 48 water bottles for a total of $18.50. At the game, he sells all of the bottles for $1.25 each. How much profit does Gavin make?
Answer: $41.50
Explanation:
$1.25 x 48 = $60.00 selling all of the water bottles
$60.00-18.50 = $41.50 (profit)
500
Find the value of x.
Answer: 105 degrees
Explanation:
S=(n-2) x 180
S= (6-2) x 180
S= 4 x 180= 720
(135+110+125+120+125)+ x = 720
615 + x = 720
x= 105 degrees