There were a total of 406 baseball cards in Caleb's baseball card collection. Binder B had 100 more baseball cards than Binder A. Binder C had 4 times as many baseball cards as Bin... There were a total of 406 baseball cards in Caleb's baseball card collection. Binder B had 100 more baseball cards than Binder A. Binder C had 4 times as many baseball cards as Binder A. a. How many baseball cards were in Binder A? b. How many baseball cards were in Binder C? Read more

Steps to Solve

1. Define Variables

Let the number of baseball cards in Binder A be represented by ( x ).

2. Express B and C in Terms of A

   • Since Binder B has 100 more baseball cards than Binder A, we can express Binder B as: $$ B = x + 100 $$

   • Binder C has 4 times as many baseball cards as Binder A, so: $$ C = 4x $$

3. Set Up the Equation for Total Cards

   • The total number of cards across all binders is given as: $$ A + B + C = 406 $$

   • Substituting the expressions for B and C into the equation, we have: $$ x + (x + 100) + 4x = 406 $$

4. Combine Like Terms

   • Combine the terms to simplify the equation: $$ 6x + 100 = 406 $$

5. Solve for x

   • Subtract 100 from both sides: $$ 6x = 306 $$

   • Divide both sides by 6: $$ x = 51 $$

6. Find the Values for B and C

   • Using ( x ) to find the number of cards in Binder B: $$ B = 51 + 100 = 151 $$

   • Using ( x ) to find the number of cards in Binder C: $$ C = 4 \times 51 = 204 $$