Questions 1-9 : Write algebraic expression for the given verbal description.
Problem 1 :
Sum of x and y.
Problem 2 :
Two times of m is decreased by 7.
Problem 3 :
3 less than 5 times of y.
Problem 4 :
One-third of the sum of three times x and y.
Problem 5 :
The sum of one-half of x and 3y.
Problem 6 :
Five-sixth of 3 less than 4 times of p.
Problem 7 :
Two less than the quotient of 3 and n.
Problem 8 :
Two less than the quotient of 3 and n.
(i) Add 5 to a number n.
(ii) Divide by 8.
(iii) Subtract by 1.
(iv) Multiply by 8.
When the sequence of operations above has been completed in order, which of the following is an expression for the statement above?
Problem 9 :
Johnny received m text messages on Friday, three less than twice as many text messages on Saturday than on Friday, and five more text messages on Sunday than on Saturday. What is the total number of text messages he received over the three days?
Problem 10 :
Twice a number is 500 more than six times the number. What is the number?
Problem 11 :
The denominator of a fraction exceeds the numerator of a fraction by 25. The value of the fraction is ⅜. Find the fraction.
Problem 12 :
If 6 times a number is decreased by 6, the result is the same as when 3 times the number is increased by 12. Find the number.
Problem 13.
Jesse earns $6 an hour babysitting for his younger brother. His mom gave him $71 last week. This included his babysitting money and his $20 allowance. How many hours did Jesse babysit?
Problem 14.
The difference between two numbers is 7. If the greater number is x to the second power, find the smaller number.
Problem 15.
A number g is decreased by 23 and then multiplied by ½. The result is 8 more than twice the number g. Find the value of g.
1. Answer :
x + y
2. Answer :
2m - 7
3. Answer :
5y - 3
4. Answer :
⅓(3x + y)
5. Answer :
(½)x + 3y
6. Answer :
⅚(4p - 3)
7. Answer :
³⁄n - 2
8. Answer :
Add 5 to a number n.
= n + 5
= ⁽ⁿ ⁺ ⁵⁾⁄₈
Subtract by 1.
= ⁽ⁿ ⁺ ⁵⁾⁄₈ - 1
= 8 ⋅ [⁽ⁿ ⁺ ⁵⁾⁄₈ - 1]
= n + 5 - 8
= n - 3
9. Answer :
Number of text messages received on Friday :
= m
Number of text messages received on Saturday (three less than twice as many text messages on Saturday than on Friday) :
= 2m - 3
Number of text messages received on Sunday (five more text messages on Sunday than on Saturday.) :
= (2m - 3) + 5
= 2m - 3 + 5
= 2m + 2
Total number of text messages Johnny received over the three days :
= m + (2m - 3) + (2m + 2)
= m + 2m - 3 + 2m + 2
= m + 2m - 3 + 2m + 2
= 5m - 1
10. Answer :
Let x be the number.
Given : Twice a number is 500 more than six times the number.
2x = 6x + 500
Subtract 6x from both sides.
-4x = 500
Divide both sides by -4.
x = -125
11. Answer :
Let x be the numerator of the fraction.
Given : The denominator of a fraction exceeds the numerator of a fraction by 25. The value of the fraction is ⅜.
ˣ⁄₍ₓ ₊ ₂₅₎ = ⅜
8x = 3(x + 25)
8x = 3x + 75
5x = 15
Divide both sides by 5.
x = 15
ˣ⁄₍ₓ ₊ ₂₅₎ = ¹⁵⁄₄₀
Therefore, the fraction is ¹⁵⁄₄₀.
12. Answer :
Let x be the number.
Given : 6 times a number is decreased by 6, the result is the same as when 3 times the number is increased by 12.
6x - 6 = 3x + 12
Subtract 3x from both sides.
3x - 6 = 12
Add 6 to both sides.
3x = 18
Divide both sides by 3.
x = 6
Therefore, the number is 6.
13. Answer :
Let x be the number of hours of babysitting.
From the information given, we have
6x + 20 = 71
Subtract 20 from both sides.
6x = 51
Divide both sides by 6.
x = 8.5
Therefore, the number of hours of babysitting was 8.5 hours.
14. Answer :
Ley y be the smaller number.
Given : The difference between two numbers is 7 and the greater number is x to the second power.
x^{2} - y = 7
Subtract x^{2 }from both sides.
-y = 7 - x^{2}
Multiply both sides by -1.
y = -7 + x^{2}
y = x^{2} - 7
Therefore, the smaller number is (x^{2} - 7).
15. Answer :
Given : A number g is decreased by 23 and then multiplied by ½. The result is 8 more than twice the number g.
½(g - 23) = 2g + 8
Multiply both sides by 2.
g - 23 = 4g + 16
Subtract 4g from both sides.
-3g - 23 = 16
Add 23 to both sides.
-3g = 39
Divide both sides by -3.
g = -13
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