Question

A granola bite contains 27 calories. Most of the calories come from c grams of carbohydrates. The rest come from other ingredients. One gram of carbohydrate contains 4 calories. The equation 4c + 5 = 27 represents the relationship between these quantities. Step 1: Answer the following questions: a. What could the 5 represent in this situation? b. Priya said that neither 8 nor 3 could be the solution to the equation. Explain why she is correct. c. Find the solution to the equation.

Answer 1

a. 5 represents the number of calories that come from other ingredients.

b. Neither 8 nor 3 satisfy the given equation, so neither 8 nor 3 can be the solution to the equation.

c. c = 5.5

Explanation:

We are given the equation:

`4c + 5 = 27`

Where
`c` represents the grams of carbohydrates

27 is the total number of calories that are received by the granola bite.

4 is the number of calories from 1 gram of carbohydrates and

5 is the number of calories that are received from other ingredients.

Answer of Part a:

5 is the number of calories that are received from other ingredients.

Part b:

Let us take left hand side (LHS) and put values of c = 8 and 3 one by one.

So, LHS becomes:

4 \times 8 + 5 = 37
`\\eq RHS\ i.e.\ 27`

4 \times 3 + 5 = 17
`\\eq RHS\ i.e.\ 27`

So, Priya is correct that neither 8 or 3 could be solution.

Part c:

`4c + 5 = 27\\\Rightarrow 4c = 22\\\Rightarrow \bold{c = 5.5}`

So, solution to the equation is: c = 5.5