Grandma gave Bryce and Carter some raisins. Bryce received 6 more raisins than Carter, and Carter received half the number of raisins Bryce received. How many raisins did Bryce receive?
Let the number of raisins Bryce received be $x$. Since Bryce received 6 more raisins than Carter, Carter received $x-6$ raisins. Since Carter received half the number of raisins Bryce did, Carter also received $x/2$ raisins. We have two ways of expressing the number of raisins Carter received, so we have the equation $x-6=x/2$, or $x=12$. Thus, Bryce received $\boxed{12}$ raisins.
12
Level 2
Prealgebra
Problem: Grandma gave Bryce and Carter some raisins. Bryce received 6 more raisins than Carter, and Carter received half the number of raisins Bryce received. How many raisins did Bryce receive?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>Let the number of raisins Carter received be denoted as C. According to the problem, Bryce received 6 more raisins than Carter, which can be expressed as B = C + 6. Additionally, it is stated that Carter received half the number of raisins Bryce received, leading to the equation C = 0.5B. 

Now, we can substitute the expression for B from the first equation into the second equation. This gives us C = 0.5(C + 6). 

To solve for C, we first distribute the 0.5: 
C = 0.5C + 3. 

Next, we isolate C by subtracting 0.5C from both sides: 
C - 0.5C = 3, 
which simplifies to 
0.5C = 3. 

Now, we multiply both sides by 2 to solve for C: 
C = 6. 

Having found the number of raisins Carter received, we can now find the number of raisins Bryce received using the first equation: 
B = C + 6 = 6 + 6 = 12. 

Thus, the final answer is 12.<|END_OF_LATENT|> The final answer is $12$.