Question

rita’s coffee shop makes a blend that is a mixture of coffee types a and b. in one bag of the blend, there are 2 kilograms of type a. five bags of the blend are a total of 50 kilograms. how many kilograms of type b are there in one bag?
(a) write an equation that could be used to answer the question above. first, choose the appropriate form. then, fill in the blanks with the numbers 2, 5, and 50. let b represent the number of kilograms of type b in one bag.
○ □(b + □) = □
○ □(b − □) = □
(b) solve the equation in part (a) to find the number of kilograms of type b in one bag.
b = □

Explanation:

Step1: Analyze the problem

We know that one bag has 2 kg of type A and \( b \) kg of type B. So one bag has \( (2 + b) \) kg. Five bags have a total of 50 kg. So the equation should be \( 5\times(2 + b)=50 \) (or equivalently \( 5\times(b + 2)=50 \)). So for part (a), we choose the \( (b + \square) \) form, with \( \square = 2 \) and the other \( \square=5 \) and the last \( \square = 50 \), so the equation is \( 5\times(b + 2)=50 \).

Step2: Solve the equation

We have the equation \( 5(b + 2)=50 \). First, divide both sides by 5: \( \frac{5(b + 2)}{5}=\frac{50}{5} \), which simplifies to \( b + 2 = 10 \). Then, subtract 2 from both sides: \( b+2 - 2=10 - 2 \), so \( b = 8 \).

Answer:

(a) The equation is \( \boldsymbol{5\times(b + 2)=50} \) (choosing the \( (b + \square) \) form, with 2 in the first blank, 5 in the second blank, and 50 in the third blank). (b) \( \boldsymbol{b = 8} \)