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valentina_108 [34]
3 years ago
13

Dakota mixes two cereals for breakfast. One gram of cereal A has 6 milligrams of sodium and 7 calories. One gram of cereal B has

8 milligrams of sodium and 5 calories. She wants the bowl of cereal to contain no more than 200 milligrams of sodium and 150 calories. Let "a" equal the number of grams of cereal A and "b" equal the number of grams in cereal B, where are "a" > 0 and "b" > 0. Which system of inequalities represents the possible ways Dakota can mix the cereals.
Mathematics
1 answer:
likoan [24]3 years ago
5 0

Number of grams of cereal A = a

Number of grams of cereal B = b

One gram of Cereal A has: 6 mg of sodium and 7 calories

One gram of Cereal A has: 8 mg of sodium and 5 calories

We need to make sure that the cereal contains maximum 200 mg sodium

⇒ Number of grams of cereal A × Sodium quantity in a gram of cereal A + Number of grams of cereal B × Sodium quantity in a gram of cereal B <= 200 mg

Substituting the required values

⇒ a×6 + b×8 <=200

Further simplifying the above equation

⇒ a×3 + b×4 <=100

Further, we need to make sure that the cereal contains maximum 150 calories

⇒ Number of grams of cereal A × Calories in a gram of cereal A + Number of grams of cereal B × Calories in a gram of cereal B <= 150

⇒ a×7 + b×5 <=150

Hence, the system of inequalities that represents the possible mix is:

a×3 + b×4 <=100 AND a×7 + b×5 <=150

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You didn't include the table but I found this table for the same statement, so I will answer you based on the next table:

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To answer the question you must find the rate for each runner and then calculate the time to run 3.1 miles at each rate.

First you need to convert the data to obtain the rate in miles per second.

These are the main conversion identities:

1 mile = 5280 feet

1 mile = 1760 yards

1 hour = 3600 seconds

1 hour = 60 minutes

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rate: 7,229 feet / 561 seconds * (1 mile / 5280 feet)  =

= 0.00244 mile/second

Time to run 3.1 miles: V = d / t => t = d / V = 3.1 miles / 0.00244 mile/second = 1270 seconds

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13 minutes + 12 seconds = 13*60 seconds +12 seconds = 792 seconds

rate = 3425 yards / 792 seconds * 1 mile / 1760 yards = 0.00246 mile/seconds

Time to run 3.1 miles = 3.1 miles / 0.00246 mile/second = 1260 seconds

Chandra:

rate = 8214 feet / 0.195 hours * 1 mile / 5280 feet * 1hour / 3600 seconds =

= 0.00222 seconds

Time = 3.1 mile / 0.00222 seconds = 0.389 hour = 1396 seconds

Divya:

rate = 1.62 miles / 732 seconds = 0.00221 seconds

Time = 3.1 mile / 0.00221 seconds = 1403 seconds

Now you can find the difference between fhe last and the first 1403 seconds - 1260 seconds = 143 seconds

That is equivalent to 2.38 seconds.
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