Scale Drawings
Quadrilateral A has side lengths 2, 3, 5, and 6. Quadrilateral B has side lengths 4, 5, 8, and 10. Could one of the quadrilaterals be a scaled copy of the other? Explain.
No. For the shortest sides to match up, the scale factor from A to B would have to be 2. But scaling the side of A with length 3 by a factor of 2 would give a side of length 6, which doesn’t match any of the side lengths of B.
Lin and her brother were born on the same date in different years. Lin was 5 years old when her brother was 2. Is there a proportional relationship between Lin’s age and her brother’s age? Explain your reasoning.
There is no proportional relationship. Every year, they each age by one year, so the ratio of their ages changes every year.
The radius of a circle is 5cm. What is its circumference?
C = 2*pi*radius = 2 * pi * 5 = 31.4 cm
A pair of designer sneakers was purchased for $120. Since they were purchased, their price has increased by 15%. What is the new price?
$138
What is -5 + 9?
4
Are two squares with the same side lengths scaled copies of one another? Explain your reasoning.
Yes. There is a scale factor of 1 between them.
The equation c=2.95g shows how much it costs to buy gas at a gas station on a certain day. In the equation, c represents the cost in dollars, and g represents how many gallons of gas were purchased.
Write down at least four (gallons of gas, cost) pairs that fit this relationship.
1,2.95; 2, 5.90; 10, 29.50; 20, 59.00
Jada paints a circular table that has a diameter of 37 inches. What is the area of the table?
About 1,075 in2
Elena’s aunt bought her a $150 savings bond when she was born. When Elena is 20 years old, the bond will have earned 105% in interest. How much will the bond be worth when Elena is 20 years old?
$307.50
150 * 1.05 + 150
What is -3 - (-9)?
6
A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building. What are the dimensions of this rectangular room in the actual building?
30 feet long and 55 feet wide
There is a proportional relationship between a volume measured in cups and the same volume measured in tablespoons. 3 cups is equivalent to 48 tablespoons.
What is the constant of proportionality for this relationship?
16 tablespoons per cup.
A car’s wheels spin at 1000 revolutions per minute. The diameter of the wheels is 23 inches. You want to know how fast the car is traveling.
Would you need to calculate area or circumference to solve this problem?
Circumference. The circumference of the wheels and the number of revolutions per minute tells you how far the car is traveling and this can be used to calculate the speed.
At a dinner, the meal cost $22 and a sales tax of $1.87 was added to the bill.
What is the tax rate for meals in this city?
8.5%, because 1.87/22 = 0.085
What is -11 * -9 * -2?
-198
A scale drawing of a car is presented in the following three scales. Order the scale drawings from smallest to largest. Explain your reasoning. (There are about 1.1 yards in a meter, and 2.54 cm in an inch.)
a. 1 in to 1 ft
b. 1 in to 1 m
c. 1 in to 1 yd
b, c, a (a meter is 39.37 inches)
A student argues y=x/9 does not represent a proportional relationship between x and y because we need to multiply one variable by the same constant to get the other one and not divide it by a constant. Do you agree or disagree with this student?
Disagree. Dividing by 9 is the same as multiplying by 1/9. We can look at the equation y=x/9 as y = 1/9*x.
A circle’s circumference is approximately 76 cm. Estimate the radius, diameter, and area of the circle.
The radius is approximately 12 cm. The diameter is approximately 24 cm. The area is approximately 460 cm2.
In a video game, Clare scored 50% more points than Tyler. If c is the number of points that Clare scored and t is the number of points that Tyler scored, which equations are correct? Select all that apply.
a. c = 1.5t
b. c = t + 0.5
c. c = t + 0.5t
d. c = t + 50
e. c = (1+0.5)t
A, C, E
What is 132 / -11?
-12
Lin has a drawing with an area of 20in2. If she increases all the sides by a scale factor of 4, what will the new area be?
320 in2 because 20*4*4=320
Every package of a certain toy also includes 2 batteries.
Use t for the number of toys and b for the number of batteries to write two equations relating the two variables.
b= t=
b = 2t and t = 0.5b
The Carousel on the National Mall has 4 rings of horses. Kiran is riding on the inner ring, which has a radius of 9 feet. Mai is riding on the outer ring, which is 8 feet farther out from the center than the inner ring is. In one rotation of the carousel, how much farther does Mai travel than Kiran?
About 106.8-56.5, or 50.3 feet farther
Tyler's mom purchased a savings bond for Tyler. The value of the savings bond increases by 4% each year. One year after it was purchased, the value of the savings bond was $156. Find the value of the bond when Tyler's mom purchased it. Explain your reasoning.
Represent the situation using the equation 1.04x=156, where x represents the value of the savings bond when Tyler's mom purchased it. The solution is x=156/1.04=150, so the bond was originally worth $150.
d * 24 = -12
d = ?
d = -1/2