Math Help Please

Sarah Meehan blends coffee for tasti-delight. She needs to prepare 190 pounds of blended coffee beans selling for $3.95 per pound. She plans to do this by blending together a high quality bean costing $5.00 per pound and a cheaper bean at $2.50 per pound. To the nearest pound, find how much high quality coffee bean and how much cheaper coffee bean she should blend.

Solution

Let h = the amount of high quality coffee beans and let c = the amount of cheaper coffee beans.

Then, since she needs to get a total of 190 pounds, h + c = 190

At this point, the problem isn’t really worded correctly because it says she wants to sell the coffee blend she gets for $3.95/lb. Perhaps it should have said that she wants the new blend to COST $3.95 per pound. Assuming that’s the case, 190 * 3.95 would mean that the total cost of the blend is $750.50. That means that 5.00(h) + 2.50(c) = 750.50

Now you have two equations with two unknowns and you can solve them in a variety of ways. An easy way is to use substitution. Take the first equation (h + c = 190) and subtract h from both sides to get c = 190 – h

Since 190 – h and c are the same, you can plug “190 – h” into the other equation wherever you see c. That becomes:

5.00(h) + 2.50(190 – h) = 750.50. Now, solve for h by combining like terms. Once you get the answer for h, plug it back into the equation c = 190 – h to find c.