# Algebra - problems - page 105

1. Simplify
Simplify expression - which expression is equivalent to: 3(m + 2) − 4(2m − 9)
2. The average
The average of one set of 4 numbers is 35. The average of another set of number is 20. The average of the numbers in the two sets is 30. How many numbers are there in the other set?
3. Boats
Three-quarters of boats are white, 1/7 are blue and 9 are red. How many boats do we have?
4. A number
A number increased by 7.9 is 8.3
5. A rectangular patio
A rectangular patio measures 20 ft by 30 ft. By adding x feet to the width and x feet to the length, the area is doubled. Find the new dimensions of the patio.
6. Perctentages
35% of what number is 35?
7. The crime
The crime rate of a certain city is increasing by exactly 7% each year. If there were 600 crimes in the year 1990 and the crime rate remains constant each year, determine the approximate number of crimes in the year 2025.
8. Find the sum
Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5
9. Sides of triangle
Triangle circumference with two identical sides is 117cm. The third side measures 44cm. How many cms do you measure one of the same sides?
10. Triangle 42
Triangle BCA. Angles A=119° B=(3y+14) C=4y. What is measure of triangle BCA=?
11. Equation 20
In given equation: 8/9-4/5=2/9+x, find x
12. MG=7x-15,
MG=7x-15, FG=33, x=? Point M is the midpoint of FG. Find unknown x.
13. Completing square
Solve the quadratic equation: m2=4m+20 using completing the square method
14. Find the 7
Find the number that is smaller than 5 5/12 by as much as 2 2/13 is smaller than 6 1/6
15. Two numbers 7
The sum of two consecutive even numbers is 30. Find the numbers.
16. Evening shift
While working the evening shift, Officer K took 8 hours to complete a task at his work station and Officer M took 10 hours to complete the same task at his work station. How many hours would it take Officer K and Officer M to complete the same task working
17. Simple equation 6
Solve equation with one variable: X/2+X/3+X/4=X+4
18. Toys 3
Tiffany's toyshop received a shipment of 360 toys. The first day 12 were sold the second day 19 were sold and on the third day, 26 was sold. How many days will the toyshop run out of toys?
19. Eq with reciprocal
Solve given equation with reciprocal member: a-6/a+10=4/8
20. Substitution method
Solve goniometric equation: sin4 θ - 1/cos2 θ=cos2 θ - 2

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