Respuesta :
We are given that Amanda made 141 pounds of coffee. If "x" is the pounds of type A coffee and "y" is the amount of type b coffee then we can write this mathematically as:
[tex]x+y=141,(1)[/tex]We are also given that the cost of type A is $5.6 per pound and that the cost of type B is $4.55 per pound and that the total cost is $728.70, this can be written mathematically as:
[tex]5.6x+4.55y=728.7,(2)[/tex]Now, we solve for "x", first by subtracting "y" from both sides:
[tex]y=141-x[/tex]Now, we substitute the value of "y" in equation (2):
[tex]5.6x+4.55(141-x)=728.7[/tex]Now, we apply the distributive property in the parenthesis:
[tex]5.6x+641.55-4.55x=728.7[/tex]Now, we add like terms:
[tex]1.05x+641.55=728.7[/tex]Now, we subtract 641.55 from both sides:
[tex]\begin{gathered} 1.05x=728.7-641.55 \\ 1.05x=87.15 \end{gathered}[/tex]Now, we divide both sides by 1.05:
[tex]x=\frac{87.15}{1.05}[/tex]solving the operations:
[tex]x=83[/tex]Now, we substitute the value of "x" in equation (1):
[tex]\begin{gathered} y=141-83 \\ y=58 \end{gathered}[/tex]Therefore, the amount of coffee type A is 83 pounds and type B is 58 pounds.
