Question

Five times the sum of some number and three is the same as four times the same number plus twenty. What is the number?

a) 5
b) 7
c) 15
d) 10

Answer 1

The number that satisfies the equation 5(x + 3) = 4x + 20 is 5, which corresponds to option (a).

Step-by-step explanation:

The student is asking for help with a linear equation problem. We can solve this problem using algebra. Let's set up an equation based on the description: 'Five times the sum of some number and three is the same as four times the same number plus twenty.' This can be translated to the algebraic equation 5(x + 3) = 4x + 20.

Let's solve the equation step-by-step:

1. Distribute the 5 to both x and 3 in the expression 5(x + 3): 5x + 15.
2. Now, write down the full equation with distribution: 5x + 15 = 4x + 20.
3. Subtract 4x from both sides to isolate x on one side: 5x - 4x + 15 = 20.
4. Simplify by combining like terms: x + 15 = 20.
5. Finally, subtract 15 from both sides to solve for x: x = 20 - 15, which gives us x = 5.

Therefore, the number that satisfies the equation is 5.

However, after reviewing the choices (a) 5 (b) 7 (c) 15 (d) 10 provided by the student, we notice that our calculated answer 5 is not listed. We must have made an error in our calculations. Let's correct the error and repeat steps 1-5:

1. 5x + 15 = 4x + 20.
2. Subtract 4x from both sides: 5x - 4x + 15 = 4x - 4x + 20, which simplifies to x + 15 = 20.
3. Subtract 15 from both sides: x + 15 - 15 = 20 - 15.
4. Now we have x = 5, which indeed coincides with option (a).

Thus, the correct answer is 5, corresponding to option (a).