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McGraw-Hill Math Grade 7 Answer Key Lesson 13.3 Rates
Exercises Solve
Question 1.
The two rectangles are similar (proportional). Given the information about rectangle EFGH, what is the length of side CD?
Answer:
The above two rectangles ABDC and EFGH are similar (proportional).
Consider length of the side CD = x
BD/CD = FG/ GH
30/x = 6/16
To find the x value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
30 × 16 = 6 × x
480 = 6x
Divide both sides of the equation by 6.
480/6 = 6x/6
80 cm = x
Length of the side CD is equal to 80 cm.
Question 2.
George likes to sweeten his ice tea. When he drinks a 20-ounce ice tea, he puts in two teaspoons of sugar. If he is making a gallon of ice tea, how many teaspoons of sugar should he add?
Answer:
We know that 1 gallon is equal to 128 ounces.
20/2 = 128/x
To find the x value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
20 × x = 128 × 2
20 x = 256
Divide both sides of the equation by 20.
20x/20 = 256/20
x = 12.8 teaspoons
If George makes a gallon of ice tea, he will add 12.8 teaspoons of sugar.
Question 3.
The two triangles are similar. Calculate the length of side s.
Answer:
The above two triangles are similar.
3/9 = 2/s
To find the s value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
3 × s = 2 × 9
3s = 18
Divide both sides of the equation by 3.
3s/3 = 18/3
s = 6
Length of the side s is equal to 6.
Question 4.
Chuck took a long hike where he started at point B and followed the path in the diagram shown. If Chuck wants to take a shorter hike where he starts at B and walks 4 miles east, turns and walks 3 miles north and then returns to point B, how long B would his last leg be? Solve this problem using proportions even though you can solve it using the Pythagorean Theorem.
Answer:
Consider chuck last leg as x.
6.25/5 = x/4
To find the x value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
6.25 × 4 = x × 5
25 = 5x
Divide both sides of the equation by 5.
25/5 = 5x/5
x = 5