How many pounds of gourmet candy selling for $2.20 per pound should be mixed with 6 pounds of gourmet candy selling for $1.20 per pound to obtain a mixture selling for $1.60 per pound?

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How many pounds of gourmet candy selling for $2.20 per pound should be mixed with 6 pounds of gourmet candy selling for $1.20 per pound to obtain a mixture selling for $1.60 per pound?

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Answer 1 · 2016-02-05T16:11:52

$$1.20 candy amount is 6 lb$ $color(green)("$1.20 candy amount is "6"lb"$
$$2.20 candy amount is 4 lb$ $color(green)("$2.20 candy amount is "4"lb"$

Explanation:

Tony B

There are two ways of solving this.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Method 1$ $color(blue)("Method 1")$

$Straight line graph approach$ $color(Brown)("Straight line graph approach")$

Standard form equation $\to y = m x + c$ $" "->y=mx+c$

In this case: $c = 1.2; m = \frac{2.20 - 1.20}{100} = \frac{1}{100}; y = 1.60$ $" "c=1.2"; "m=(2.20-1.20)/100 = 1/100"; "y=1.60$

$1.6 = \frac{x}{100} + 1.2$ $1.6=x/100+1.2$

$x = (1.6 - 1.2) \times 100 \to x = 0.4 \times 100$ $x=(1.6-1.2)xx100" "color(purple)(-> x=0.4xx100)$

$x = 40 \to 40 %$ $x=40-> 40%$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Method 2$ $color(blue)("Method 2")$

$Ratios, which is the same thing as method 1 just that this fact is in disguise.$ $color(Brown)("Ratios, which is the same thing as method 1 just that this fact is in disguise.")$

The approach is based on the principle that the gradient is constant.

$\frac{100}{2.2 - 1.2} = \frac{x}{1.6 - 1.2}$ $100/(2.2-1.2)=x/(1.6-1.2)$

Basically this is saying that the gradient of the whole is the same gradient as part of it!

$\frac{100}{1} = \frac{x}{0.4}$ $100/1=x/0.4$

$0.4 \times 100 = x$ $color(purple)(0.4xx100=x)$

$x = 40 \to 40 %$ $x=40" " -> 40%$

$color(green)('"NOTE THAT IS 40% OF THE $2.20 CANDY")$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("Determine the weights of each constituent")$

so $100%-40% =60%$ as the proportion of the $1.20 candy

Let the whole weight be $w$ then

$60/100 w=6$

$w=(6xx100)/60" "=" "100/10" "=" "10lb$

So

$color(green)("$1.20 candy amount is "6"lb"$
$color(green)("$2.20 candy amount is "10-6 = 4"lb"$

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How many pounds of gourmet candy selling for $2.20 per pound should be mixed with 6 pounds of gourmet candy selling for $1.20 per pound to obtain a mixture selling for $1.60 per pound?

1 Answer

Explanation:

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