A mixture of 30 pounds of candy sells for $1.10 a pound. The mixture consists of chocolates worth $1.50 a pound and chocolates worth 90 cents a pound. How many pounds of the $1.50 chocolate were used to make the mixture?

1 Answer
Jun 18, 2017

Answer:

There are 10 pounds of the more expensive chocolate that costs $1.50 and 20 pounds of the cheaper chocolate that costs $0.90.

Explanation:

Call the number of pounds of the $1.50 chocalate 'e' (for 'expensive') and the number of pounds of the $0.90 chocolate 'c'. (we need to express both in dollars)

We know that #e + c = 30# (Equation 1) because there are 30 pounds of chocolate in total. We also know that:

#exx1.5+cxx0.9=30xx1.1#

We can write that as:

#1.5e+0.9c=33# (Equation 2)

Now we have two equations with two unknowns, so we will use our skills in solving 'simultaneous equations'. We can rearrange Equation 1 to give us a value for #c# in terms of #e#:

#c=30-e#

Now we substitute that value into Equation 2:

#1.5e+0.9(30-e)=33#

#1.5e+27-0.9e=33#

#0.6e=6#

#e=10# pounds

In this case, since we know the total is 30 pounds, it's easy to reason that #c=20# pounds, but we could also calculate that result by substituting our value for #e# back into Equation 1.

This result makes sense, since the final price is closer to the cheaper than the more expensive price, because there is more of the cheaper chocolate included.