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2.05 Applications of Linear Equations

Write an equation for each problem. Work backwards to solve the equation. Show ALL solution steps.

1. A number is multiplied by 7, and then the product is added to 13. The result is 55. What is the number?

     

2. The English alphabet contains 2 more than twice as many letters as the Hawaiian alphabet. How many letters are there in the Hawaiian alphabet?

     

3. A number is divided by 4, and then the quotient is added to 17. The result is 25. Find the number.

     

Write and solve an equation for each problem. Show ALL solution steps.

4. On May 14, 1898, a severe hailstorm hit Kansas City. The largest hailstones were 9.5 inches in circumference. Find the radius of one of the largest hailstones. The formula for the circumference of a circle is C = 2πr.

     

5. The formula for the area of a triangle is A = ½ bh.

a. Find the area of a triangle with a base of 18 feet and a height of 7 feet.

     

b. Solve the formula for h. Find the height of a triangle with an area of 28 feet2 and a base of 8 feet.

     

6. The formula for finding area of a trapezoid is A = ½ (b1 + b2)h.

a. Solve the formula for h, and find the height of a trapezoid with an area of 60 m2 and bases of 8m and 12m.

     

7. The formula used to find the volume of a rectangular prism is V =lwh.

a. Solve the formula for w, and find the width of a rectangular prism that has a length of 10m, a height of 14m, and an overall volume of 1890m3.

     

8. Marco traveled 5 hours at a constant rate to cover a total of 320 miles. Use the formula, d = rt, that relates distance, rate, and time to find Marco’s rate of travel.

     

9. Jayla recently accepted a new job earning $15.50 per hour. Last month, Jayla earned $2294 after four weeks of work. How many hours did Jayla work each week?

     

10. Keila traveled at the constant rate of 72 miles per hour for a total of 414 miles. Use the formula, d = rt, that relates distance, rate, and time to find the number of hours Keila traveled.

     

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