Question 124567
Start by letting x = the number of pounds of the $0.50 per pound coffee.
The the number of pounds of the $0.08 per pound coffee can be expressed by (x+10)
The sum of these two quantities (x+x+10)is to equal the number of pounds of coffee at $0.70 per pound.
We can write the following equation:
{{{(0.50)x + (0.80)(x+10) = (x+x+10)(0.70)}}} Simplify this and solve for x.
{{{0.5x+0.8x+8 = 0.7(2x+10)}}}
{{{1.3x+8 = 1.4x+7}}} subtract 1.3x from both sides.
{{{8 = 0.1x+7}}} Subtract 7 from both sides.
{{{1 = 0.1x}}} Divide both sides by 0.1
{{{10 = x}}}
The dealer will need to mix 10 pounds of the $0.50 per pound coffee (x+10) 20 pounds of the $0.80 per pound coffee to obtain 30 pounds of $0.70 per pound coffee.