Question 704816
Let A = pounds of cheese that costs $3.75/pound
Let B = pounds of cheese that costs $4.55/pound
Equation 1:{{{A + B = 45}}} (A 45 pound block of mixed cheese)
Equation 2:{{{(3.75*A + 4.55*B)/(A+B) = 4.05}}} (The cost per pound of the mixed cheese block)
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Solve Equation 1 for one of the variables.
Equation 1:{{{A + B = 45}}}
{{{A = 45 - B}}}
Now plug (45 - B) into Equation 2 for A
Equation 2:{{{(3.75*A + 4.55*B)/(A+B) = 4.05}}}
{{{(3.75*(45 - B) + 4.55*B)/((45 - B)+ B) = 4.05}}}
Multiply the 3.75 trough and simplify the equation
{{{(168.75 - 3.75B + 4.55B)/(45) = 4.05}}}
Multiply both sides by 45
{{{168.75 - 3.75B + 4.55B = 182.25}}}
Combine like terms
{{{168.75 + 0.8B = 182.25}}}
Subtract 168.75 from both sides
{{{0.8B = 13.5}}}
Divide both sides by 0.8
{{{highlight(B = 16.875)}}}
Now plug 16.875 into equation 1 for B
Equation 1:{{{A + B = 45}}}
{{{A + (16.875) = 45}}}
{{{highlight_green(A = 28.125)}}}