A bakery can make 42 cheesecakes for every 6 blocks of cream cheese. Which table represents the relationship between the number of cheesecakes the bakery makes and the number of bl... A bakery can make 42 cheesecakes for every 6 blocks of cream cheese. Which table represents the relationship between the number of cheesecakes the bakery makes and the number of blocks of cream cheese the bakery uses? Read more

Steps to Solve

1. Understand the Given Ratio The relationship given is that 42 cheesecakes are made using 6 blocks of cream cheese. We can write this as a ratio:
   $$ \text{Cheesecakes} : \text{Cream Cheese} = 42 : 6 $$

2. Simplify the Ratio To work easily with ratios, we can simplify it by dividing both numbers by their greatest common divisor, which is 6:
   $$ \frac{42 \div 6}{6 \div 6} = \frac{7}{1} $$ This means for every 7 cheesecakes, 1 block of cream cheese is used.

3. Set Up the Relationship Now we can express the number of cheesecakes ($C$) and the number of blocks of cream cheese ($B$) with the relationship derived:
   $$ C = 7B $$
   To verify tables, we will be checking if the number of cheesecakes is 7 times the number of cream cheese blocks.

4. Evaluate Each Table Now, we need to check each table to see if the corresponding values meet the derived relationship:

• Table A:

  • 1 cheesecake → 7 blocks (Wrong)
  • 2 cheesecakes → 14 blocks (Wrong)
  • 3 cheesecakes → 21 blocks (Wrong)

• Table B:

  • 6 cheesecakes → 1 block (Correct: $6 \div 1 = 6$, not 7)
  • 12 cheesecakes → 2 blocks (Correct: $12 \div 2 = 6$, not 7)
  • 18 cheesecakes → 3 blocks (Correct: $18 \div 3 = 6$, not 7)

• Table C:

  • 1 cheesecake → 6 blocks (Wrong)
  • 2 cheesecakes → 12 blocks (Correct: $2 \div 12 = 6$, not 7)
  • 3 cheesecakes → 18 blocks (Wrong)

• Table D:

  • 7 cheesecakes → 1 block (Correct: $7 \div 1 = 7$, matches)
  • 14 cheesecakes → 2 blocks (Correct: $14 \div 2 = 7$, matches)
  • 21 cheesecakes → 3 blocks (Correct: $21 \div 3 = 7$, matches)

5. Identify the Correct Table Table D satisfies the ratio of cheesecakes to cream cheese, as all rows maintain the relationship $C = 7B$.