Finding Consecutive Numbers Algebraically
Let the four consecutive numbers be represented as $x$, $x+1$, $x+2$, and $x+3$.
The problem states that twice the first, three times the second, four times the third, and five times the fourth sum up to 236. This can be written as an equation:
$2x + 3(x+1) + 4(x+2) + 5(x+3) = 236$
Solving the Algebraic Equation
- Expand the terms: $2x + 3x + 3 + 4x + 8 + 5x + 15 = 236$
- Combine like terms (the $x$ terms and the constant terms): $(2x + 3x + 4x + 5x) + (3 + 8 + 15) = 236$ $14x + 26 = 236$
- Isolate the variable term by subtracting 26 from both sides: $14x = 236 - 26$ $14x = 210$
- Solve for $x$ by dividing both sides by 14: $x = \frac{210}{14}$ $x = 15$
Determining the Consecutive Numbers
Since the first number ($x$) is 15, the four consecutive numbers are:
- First number: $x = 15$
- Second number: $x+1 = 15+1 = 16$
- Third number: $x+2 = 15+2 = 17$
- Fourth number: $x+3 = 15+3 = 18$
The four consecutive numbers are 15, 16, 17, and 18.
Verification: $2(15) + 3(16) + 4(17) + 5(18) = 30 + 48 + 68 + 90 = 236$. The condition is satisfied.
The correct option is 15, 16, 17, 18.
Similar Questions
- Find the value of x satisfying: $2(3x^2 - 7) - 3(2x^2 + 7x - 9) = 13$
- If $(1 + 2 + \text{x}) - (0.12 - 0.42 + 0.94) = 4$, then what will be the value of x?
- Find the value of x satisfying: $5(5x^2 - 6) - 5(5x^2 + 2x - 4) = 20$
- The sum of half, one-third and one-fifth of a number exceeds the number by $12$. What is the number?
- Sonal was given some money to take care of her travel expenses during a 16-day sales drive. However, she had to increase her stay by another 8 days, and as a result her average daily travel allowance went down by ₹80. How much was sanctioned to her in the beginning?
- Anushka has kept four erasers, some pencils and some sharpeners in a bag. The number of sharpeners is one-fourth of the number of pencils. How many pencils does she have, if the total number of the three items is 49?
- Find the value of x.
$6(8x + 25) - 70 = 5(8x + 25)$ - If $11 = \frac{11x}{1 - x}$, then the value of $(2x)^2$ is:
- Find the number whose four-fifth is more than its three-fourth by 4.
- When 38 is added to $30\%$ of a number. The result is 50. What is the number?
Important Questions from Linear Equation in 1 Variable
The sum of three fractions A, B, and C, A > B > C, is \(\frac{121}{60}\) . When C is divided by B, the resulting fraction is \(\frac{9}{10}\) , which exceeds A by \(\frac{3}{20}\) . What is the difference between B and C?
7 is added to a certain number and the sum is multiplied by 5. The product is then divided by 3 and 4 is subtracted from the quotient. If the result comes to 16, then what is the original number?
If the measure of one angle of a right triangle is 30° more than the measure of the smallest angle, then the measure of the smallest angle is:
A man has equal number of five, ten and twenty rupee notes amounting to Rs. 385. Find the total number of notes?
The sum of three consecutive number is 126. Find the highest number?
