Question

select the correct answer.
jonathan collects postcards and stamps. the number of postcards in his collection is 12 more than \\( \frac{3}{4} \\) the number of stamps. he has 39 postcards in all.
if jonathan has \\( x \\) stamps, which equation represents this situation and how many stamps does he have?
a. the equation is \\( \frac{3}{4}x + 12 = 39 \\), and the number of stamps is 36.

b. the equation is \\( \frac{3}{4}x + x = 39 \\), and the number of stamps is 24.

c. the equation is \\( x + \frac{3}{4} + x = 39 \\), and the number of stamps is 18.

d. the equation is \\( \frac{3}{4}x = 39 + x \\), and the number of stamps is 156.

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Explanation:

Step1: Define variables and relationships

Let \( x \) be the number of stamps. The number of postcards is 12 more than \( \frac{3}{4}x \), so postcards \( = \frac{3}{4}x + 12 \). Total items (postcards + stamps) is 39, so equation: \( \frac{3}{4}x + 12 + x = 39 \)? Wait, no—wait, the problem says "He has 39 postcards in all"? Wait, no, re-reading: "Jonathan collects postcards and stamps. The number of postcards in his collection is 12 more than \( \frac{3}{4} \) the number of stamps. He has 39 postcards in all. If Jonathan has \( x \) stamps, which equation represents this situation and how many stamps does he have?"

Wait, correction: Postcards = 12 + \( \frac{3}{4}x \), and postcards = 39. So equation: \( \frac{3}{4}x + 12 = 39 \). Then solve for \( x \):

Step2: Solve the equation \( \frac{3}{4}x + 12 = 39 \)

Subtract 12: \( \frac{3}{4}x = 39 - 12 = 27 \)

Multiply by \( \frac{4}{3} \): \( x = 27 \times \frac{4}{3} = 36 \)

Now check options:

A. Equation \( \frac{3}{4}x + 12 = 39 \), stamps 36. Correct.

B. Equation \( \frac{3}{4}x + x = 39 \) (wrong, postcards are 39, not total), solve: \( \frac{7}{4}x=39 \), \( x \approx 22.29 \), not 24.

C. Equation \( x + \frac{3}{4} + x = 39 \) (wrong, no, postcards are 12 + 3/4 x), solve: \( 2x + 0.75 = 39 \), \( x \approx 19.125 \), not 18.

D. Equation \( \frac{3}{4}x = 39 + x \) (wrong, postcards can't be less than total), solve: \( -\frac{1}{4}x = 39 \), \( x = -156 \) (invalid).

So A is correct.

Answer:

A. The equation is \(\frac{3}{4}x + 12 = 39\), and the number of stamps is 36.