How do you create your equations when working on a mixture word problem?
Let's try to think about the general form of a word problem involving mixtures.
In general, we have the following scenario:
a merchant sells two kinds of products (coffee, sweets, etc).
we know the unit prices for both kinds of products and for the final mixture
p
1
US dollars per pound for the first kind of product,
p
2
US dollars per pound for the second kind of product
p
m
US dollars per pound for the mixture
we know the total quantity formed by the mixture of the two products (
q
pounds)
we have to find out the quantities of each product needed to form the mixture
(here we have the variables:
x
denoting the quantity of the first kind of product and
y
denoting the quantity of the second kind of product)
Now, we have sufficient information to work out the equations.
First, we know that the sum of the two quantities is
q
pounds, which gives us the first equation:
x
+
y
=
q
Second, we know that the sale price is the product of quantity and unit price, which gives us the second equation:
p
1
x
+
p
2
y
=
p
m
⋅
q
Now, we have a system of two linear equations that can be easily solved by substitution.
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