Question

If almonds sell at \[\$ 3.60\] per pound and walnuts sell for \[\$ 2.25\] pound, how many pounds of each must be used to make $45$ pounds of a mixture to sell at \[\$ 3.00\] per pound?

Answer 1

Hint: To find the amounts of almonds and walnuts which are to be used, you have to first consider the amount of almond and walnut to be and variable and with use of the information given in the question, write equations with variables. You will get two equations to solve the equations for the value of variables to get the required amount of almond and coconut.

Complete step by step solution:
In order to find the amounts of almonds and walnuts, let us first consider that there are $x$ pounds of almonds and $y$ pounds of walnuts are required.So now,according to the question, we can write that
$x + y = 45 - - - - (i)$
Also, total selling cost will be $\$ 3.00 \times 45 = \$ 135.00$
Using this we can write that
$3.6x + 2.25y = 135 - - - - (ii)$
From equation (i),
$x + y = 45 \\
\Rightarrow x = 45 - y - - - - (iii) \\ $
Substituting $x = 45 - y$ in equation (ii), we will get
$3.6(45 - y) + 2.25y = 135 \\
\Rightarrow 162 - 3.6y + 2.25y = 135 \\
\Rightarrow 162 - 1.35y = 135 \\
\Rightarrow 1.35y = 162 - 135 \\
\Rightarrow 1.35y = 27 \\
\Rightarrow y = \dfrac{{27}}{{1.35}} \\
\Rightarrow y = 20 $
So we get $y = 20$, to find the value of the other variable, we will put value of $y$ in the third equation as follows
$x = 45 - 20 \\
\therefore x = 25 \\ $
Therefore $25$ pound almonds and $20$ pound of walnuts is required for the given condition in the question.

Note:When solving this type of word problem, the best and first step should be to consider the required amount to be a variable and then make equations further with help of given information. So reading and understanding the question is also crucial because one will write incorrect equations if he doesn’t understand the problem.