Simple Algebraic Equation
A simple algebraic equation contains a single variable (usually written as "x" or any alphabetic word)
1. Q: The sum of 20 and twice an unknown number is 70. The unknown number is...
Answer:
Let the unknown number as "x". So, we can write the equation based on the problem:
[tex]\boxed{20 + 2x = 70}[/tex]
Find the value of "x" using algebraic operation
[tex]20 + 2x = 70\\2x = 70 - 20\\2x = 50\\x = 25[/tex]
Hence, the value of the unknown number is 25
2. Q: A string of length 120 cm is cut into 2 pieces. One piece is 30 cm shorter than the other. The length of the longer piece is
Answer:
Let the longer piece as "x". So, we can write the equation based on the problem:
[tex]\boxed{120 = x + (x - 30)}[/tex]
Find the value of "x" using algebraic operation
[tex]120 = x + x - 30\\120 = 2x - 30\\120 + 30 = 2x\\150 = 2x\\x = 75[/tex]
Hence the length of the other piece is 75 cm
3. Q: In a bus of 54 passengers, the number of adults is 5 times the number of children. Find the number of the adults
Answer:
Let the number of children as "x". So, we can write the equation based on the problem:
[tex]\boxed{54 = x + 5x}[/tex]
Find the value of "x" using algebraic operation
[tex]54 = x + 5x\\54 = 6x\\x = 9[/tex]
The number of children is 9. Hence, there are 45 adults (from 9 × 5)
4. Q: Wire A is w m long. Wire B is twice as long as Wire A. Wire C is 3 m shorter than Wire B. If the total length of the three wires is 32 m, how long is Wire A?
Answer:
Let the length of wire A as "w", So..
A = w m
B = 2w m
C = 2w - 3 m
*) m stand for "meter"
So, we can write the equation based on the problem
[tex]\boxed{32 = w + 2w + (2w - 3)}[/tex]
To find the value of "w", use algebraic operation
[tex]32 = w + 2w + (2w - 3)\\32 = 3w + (2w - 3)\\32 = 3w + 2w - 3\\32 = 5w - 3\\32 + 3 = 5w\\35 = 5w\\w = 7[/tex]
Hence, the length of wire A is 7 meter
5. Q: There are x people on the train. At the next station, 37 people get off and 12 people get on. How many people are on the train now in terms of x?
Answer:
Let the people on the train as "x", so the equation to find the amount of people on that problem is
[tex]x - 37 + 12\\x - 25[/tex]
Hence, there are x - 25 people onboard right now
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Details:
Subjects: Mathematics
Topic: Algebra
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