Compare Ratios Practice
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Question
The following tables show the amount of sodium for a given number of crackers for two types of crackers. Which type of cracker has less sodium per cracker?
Cracker 1
Milligrams of Sodium Number of Crackers
520 20
1,040 40
1,560 60
2,080 80
2,600 100
3,120 120
Cracker 2
Milligrams of Sodium Number of Crackers
200 16
400 32
600 48
800 64
1,000 80
1,200 96(1 point)
Cracker
has less sodium per cracker.
To compare which type of cracker has less sodium per cracker, we need to calculate the ratio of milligrams of sodium to the number of crackers for each type of cracker.
For Cracker 1:
- The ratio for 20 crackers is 520/20 = 26 mg/cracker
- The ratio for 40 crackers is 1040/40 = 26 mg/cracker
- The ratio for 60 crackers is 1560/60 = 26 mg/cracker
- The ratio for 80 crackers is 2080/80 = 26 mg/cracker
- The ratio for 100 crackers is 2600/100 = 26 mg/cracker
- The ratio for 120 crackers is 3120/120 = 26 mg/cracker
For Cracker 2:
- The ratio for 16 crackers is 200/16 = 12.5 mg/cracker
- The ratio for 32 crackers is 400/32 = 12.5 mg/cracker
- The ratio for 48 crackers is 600/48 = 12.5 mg/cracker
- The ratio for 64 crackers is 800/64 = 12.5 mg/cracker
- The ratio for 80 crackers is 1000/80 = 12.5 mg/cracker
- The ratio for 96 crackers is 1200/96 = 12.5 mg/cracker
From the calculations above, it is clear that both Cracker 1 and Cracker 2 have the same amount of sodium per cracker, which is 26 mg/cracker and 12.5 mg/cracker, respectively. So, both types of crackers have the same amount of sodium per cracker.
To find out which type of cracker has less sodium per cracker, we need to compare the ratios of milligrams of sodium to the number of crackers for each type of cracker.
For Cracker 1:
Ratio = milligrams of sodium / number of crackers
For the first data point, the ratio is: 520 mg / 20 crackers = 26 mg/cracker
For the second data point, the ratio is: 1040 mg / 40 crackers = 26 mg/cracker
For the third data point, the ratio is: 1560 mg / 60 crackers = 26 mg/cracker
For the fourth data point, the ratio is: 2080 mg / 80 crackers = 26 mg/cracker
For the fifth data point, the ratio is: 2600 mg / 100 crackers = 26 mg/cracker
For the sixth data point, the ratio is: 3120 mg / 120 crackers = 26 mg/cracker
Therefore, the ratio remains constant at 26 mg/cracker for Cracker 1.
For Cracker 2:
Ratio = milligrams of sodium / number of crackers
For the first data point, the ratio is: 200 mg / 16 crackers = 12.5 mg/cracker
For the second data point, the ratio is: 400 mg / 32 crackers = 12.5 mg/cracker
For the third data point, the ratio is: 600 mg / 48 crackers = 12.5 mg/cracker
For the fourth data point, the ratio is: 800 mg / 64 crackers = 12.5 mg/cracker
For the fifth data point, the ratio is: 1000 mg / 80 crackers = 12.5 mg/cracker
For the sixth data point, the ratio is: 1200 mg / 96 crackers = 12.5 mg/cracker
Therefore, the ratio remains constant at 12.5 mg/cracker for Cracker 2.
Comparing the ratios, we can see that Cracker 2 has less sodium per cracker at 12.5 mg/cracker, compared to Cracker 1 which has 26 mg/cracker.
To determine which type of cracker has less sodium per cracker, you need to calculate the ratio of sodium to the number of crackers for each type of cracker.
For Cracker 1:
- Divide the milligrams of sodium by the number of crackers for each row in the table.
- Calculate the ratio for each row:
- 520 mg sodium / 20 crackers = 26 mg/cracker
- 1,040 mg sodium / 40 crackers = 26 mg/cracker
- 1,560 mg sodium / 60 crackers = 26 mg/cracker
- 2,080 mg sodium / 80 crackers = 26 mg/cracker
- 2,600 mg sodium / 100 crackers = 26 mg/cracker
- 3,120 mg sodium / 120 crackers = 26 mg/cracker
For Cracker 2:
- Divide the milligrams of sodium by the number of crackers for each row in the table.
- Calculate the ratio for each row:
- 200 mg sodium / 16 crackers = 12.5 mg/cracker
- 400 mg sodium / 32 crackers = 12.5 mg/cracker
- 600 mg sodium / 48 crackers = 12.5 mg/cracker
- 800 mg sodium / 64 crackers = 12.5 mg/cracker
- 1,000 mg sodium / 80 crackers = 12.5 mg/cracker
- 1,200 mg sodium / 96 crackers = 12.5 mg/cracker
Comparing the ratios, we can see that Cracker 2 has less sodium per cracker with a consistent ratio of 12.5 mg/cracker, while Cracker 1 has a consistent ratio of 26 mg/cracker. Therefore, Cracker 2 has less sodium per cracker.