Question

Chang's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Chang $5.65 per pound,and type B coffee costs $4.30 per pound. This month, Chang made 162 pounds of the blend, for a total cost of $826.20.How many pounds of type B coffee did he use?

Answer 1

STEP 1: Interprete the statements

Chang made 162 pounds which involve a mix of both, which means

$A+B=162$

Also, since A cost 5.65 and B cost 4.30. The total cost is 826.20

$5.65A+4.30B=826.20$

Step 2: Solve the equations simultaneously.

$\begin{gathered} Use\text{ elimination method} \\ A+B=162 \\ 5.65A+4.30B=826.20 \\ This\text{ implies that } \\ A=162-B \\ We\text{ substituute A=162-B in equation 2} \\ 5.65(162-B)+4.30B=826.20 \\ 915.3-5.65B+4.30B=826.20 \\ \text{Collect like terms} \\ 5.65B-4.30B=915.3-826.20 \\ 1.35B=89.1 \\ \text{Divide both side by 1.35} \\ B=\frac{89.1}{1.35} \\ B=66 \end{gathered}$

Therefore, Chang used 66 pounds of type B coffee