Question

fernando has four times as many cards as elijah. if fernando were to give elijah seven cards, then fernando would have eight fewer cards than elijah. how many cards does fernando currently have?
a. 1
b. 4
c. 6
d. 8
e. 12

Explanation:

Step1: Define variables

Let Elijah's cards be $x$. Then Fernando's cards are $4x$.

Step2: Set up equation after giving cards

After Fernando gives 7 cards to Elijah, Fernando has $4x - 7$ and Elijah has $x + 7$. The equation is $(x + 7) - (4x - 7) = 8$.

Step3: Solve the equation

Simplify: $x + 7 - 4x + 7 = 8$ → $-3x + 14 = 8$ → $-3x = -6$ → $x = 2$.

Step4: Find Fernando's current cards

Fernando has $4x = 4\times2 = 8$? Wait, no, wait. Wait, let's re - check the equation. Wait, the problem says "Fernando would have eight fewer cards than Elijah", so Elijah's new amount minus Fernando's new amount is 8. So $(x + 7)-(4x - 7)=8$. Let's solve again: $x + 7-4x + 7 = 8$ → $-3x+14 = 8$ → $-3x=8 - 14=-6$ → $x = 2$. Then Fernando has $4x = 8$? But wait, let's check with the options. Wait, maybe I made a mistake. Wait, let's try plugging in the options. Let's try option d: 8. If Fernando has 8, Elijah has 2. After giving 7, Fernando has 1, Elijah has 9. 9 - 1 = 8. Yes! So that works. Wait, but when I solved $x = 2$, Fernando has $4x = 8$. So that's correct.

Wait, but let's do the equation again. Let $F = 4E$. After giving 7, $F - 7=(E + 7)-8$. So $F - 7=E - 1$. Since $F = 4E$, substitute: $4E-7 = E - 1$ → $3E=6$ → $E = 2$. Then $F = 8$. Yes, that's correct.

Answer:

d. 8