7th Grade Challenging Math

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7-71) ABCD is a rectangle. EFGH is a rectangle formed by 6 squares with side length of a. AE=FB=a.  Angle HID = Angle GJC = 45 degrees.  If the area of ABCD is 600 square millimeters,

a) What is the area of rectangle EFGH?

b) What is the area of HGJI?

c) Express the area of ABCD in terms of "a"

7-72) Matt has some chickens and rabbits. There are 32 feet and 10 heads in all.
How many chickens and rabbits does Matt have? Do not use simultaneous equations to solve this problem.
 

7-73) Farmer Zach has some pigs and turkeys. There are 34 heads and 76 legs in all. How many pigs and turkeys does farmer Zach have? Do not use simultaneous equations to solve this problem.

7-74) Raj attended a math competition. There are 20 multiple choice questions. Each question is worth 5 points. However, if a wrong answer is selected, 3 points are taken away. Raj answered all 20 questions and got 60 points. How many questions did he get wrong? Do not use simultaneous equations to solve this problem.
 

7-75) Jenny took a physics test. There are 30 multiple choice questions. Each question is worth 4 points. However, if a wrong answer is selected, 2 points are taken away. Jenny answered all 20 questions and got 96 points. How many questions did she get wrong? Do not use simultaneous equations to solve this problem.

 

7-76) Jackie's house, the tennis court and Nancy's house form a straight line with the tennis court between the two houses. The two houses are 3400 feet apart. The girls want to walk to the court and play tennis. Nancy walks 160 feet a minute and Jackie walks 180 feet a minute. They arrive at the tennis court at the same time. How many minutes does it take for the girls to arrive at the tennis court?

 

7-77) Andy's house, the park and Sam's house form a straight line with the park between the two houses. The two houses are 1420 feet apart. The boys want to walk to the park and play. Andy walks 60 meters a minute and Sam walks 70 meters a minute. Andy left his house 2 minutes before Sam left his, and they arrived at the park at the same time. How far is Andy's house from the park?
 

7-78) If A 8 B = 1 + 2 +3 + 4 + ..... + (A x B)

Example: 2 8 3 = 1 + 2 + 3 + 4 + 5 + (2 x 3)

Calculate (4 8 5) - (2 8 3)

7-79)  If A # B = (A x B) / (A + B)

         a) Calculate 9 # (10 # 10)

         b) Calculate 8 # (5 # 5)

7-80)   How many triangles are there?

More challenging math problems for seventh grade:
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71-80  81-90