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Sagot :
Problem no.1:
- 1.) Seven increased by three times a number is thirteen. What is the unknown number?
Solution:
The mathematical phrase "Seven increased by three times a number is thirteen" translated to an algebraic equation is 7 + 3x = 13. The "x" represents the number and the "increased by" means that you have to add three times a number from seven.
Let x represent the unknown number. Break the word problem into smaller pieces and then represent each piece by an algebraic expression.
Seven ⟹ 7
increased by ⟹ + (addition sign)
three times ⟹ 3
an unknown number ⟹ x
is ⟹ = (equal sign)
thirteen ⟹ 13
Now, lets find the unknown number to the algebraic equation above, 7 + 3x = 13.
Solve for the unknown number.
- 7 + 3x = 13
- 3x = 13 - 7
- 3x/3 = 6/3
- x = 2
Checking:
Plug in the number in the algebraic equation to check if the answer is correct.
- 7 + 3x = 13
- 7 + 3(2) = 13
- 7 + 6 = 13
- 13 = 13 ✓
Answer:
- The unknown number is 2.
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Problem no.2:
- 2.) Four times a number is equal to twice the sum of five and that number. Find the unknown number.
Solution:
The mathematical phrase "Four times a number is equal to twice the sum of five and that number" translated to an algebraic equation is 4x = 2(5 + x). The "x" represents the number and the "sum" means that you have to add a number.
Let x represent the unknown number. Break the word problem into smaller pieces and then represent each piece by an algebraic expression.
Four times ⟹ 4 •
an unknown number ⟹ x
is equal to ⟹ = (equal sign)
twice the sum of five and that unknown number ⟹ 2 • (5 + x)
Now, lets find the unknown number to the algebraic equation above, 4x = 2(5 + x).
Solve for the unknown number.
- 4x = 2(5 + x)
- 4x = 10 + 2x
- 4x - 2x = 10
- 2x/2 = 10/2
- x = 5
Checking:
Plug in the number in the algebraic equation to check if the answer is correct.
- 4x = 2(5 + x)
- 4x = 10 + 2x
- 4(5) = 10 + 2(5)
- 20 = 10 + 10
- 20 = 20 ✓
Answer:
- The unknown number is 5.
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Problem no.3:
- 3.) When seven is subtracted from six and unknown number, the result is eleven. What is the unknown number.
Solution:
The mathematical phrase "when seven is subtracted from six and unknown number, the result is eleven" translated to an algebraic equation is 6x - 7 = 11. The "x" represents the number and the "subtracted from" means that you have to subtract.
Let x represent the unknown number. Break the word problem into smaller pieces and then represent each piece by an algebraic expression.
When seven ⟹ 7
is subtracted from ⟹ - (subtract sign)
six times an unknown number ⟹ 6 • x
the result is ⟹ = (equal sign)
eleven ⟹ 11
Now, lets find the unknown number to the algebraic equation above, 6x - 7 = 11.
Solve for the unknown number.
- 6x - 7 = 11
- 6x = 11 + 7
- 6x/6 = 18/6
- x = 3
Checking:
Plug in the number in the algebraic equation to check if the answer is correct.
- 6x - 7 = 11
- 6(3) - 7 = 11
- 18 - 7 = 11
- 11 = 11 ✓
Answer:
- The unknown number is 3.
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↓↓ NOTE: ↓↓
To check a word problem, the solution must be checked in the word statement. The reason for checking in the word statement is that an error may have been made in writing the equation that would not be discovered if you substitute the solution in the equation.
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