Let's carefully analyze the information in the problem to determine the correct equation and the number of stamps Jonathan has.
Step 1: Understand the relationship between postcards and stamps.
Jonathan collects both postcards and stamps. According to the problem, the number of postcards he has is 12 more than [tex]\(\frac{3}{4}\)[/tex] the number of stamps.
Let [tex]\(x\)[/tex] represent the number of stamps Jonathan has.
The number of postcards he has can be expressed as:
[tex]\[\frac{3}{4}x + 12\][/tex]
Step 2: Set up the equation based on the given total number of postcards.
We are told that Jonathan has 39 postcards in all. This can be represented by the equation:
[tex]\[\frac{3}{4}x + 12 = 39\][/tex]
Step 3: Solve the equation for [tex]\(x\)[/tex].
To find the value of [tex]\(x\)[/tex], we need to isolate [tex]\(x\)[/tex] on one side of the equation.
1. Start with the equation:
[tex]\[\frac{3}{4}x + 12 = 39\][/tex]
2. Subtract 12 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[\frac{3}{4}x = 39 - 12\][/tex]
[tex]\[\frac{3}{4}x = 27\][/tex]
3. To solve for [tex]\(x\)[/tex], multiply both sides by the reciprocal of [tex]\(\frac{3}{4}\)[/tex], which is [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[x = 27 \times \frac{4}{3}\][/tex]
[tex]\[x = 27 \times \frac{4}{3} = 36\][/tex]
So, Jonathan has 36 stamps.
Step 4: Check the options for the correct answer.
We see that option A corresponds to the equation [tex]\(\frac{3}{4}x + 12 = 39\)[/tex] and states that the number of stamps is 36, which matches our solution.
Thus, the correct answer is:
A. The equation is [tex]\(\frac{3}{4} x + 12 = 39\)[/tex], and the number of stamps is 36.
