Question

2. Sue is buying a 13-pound mixture of gummy candy, jelly beans, and hard candy. The cost of gummy candy is $1.20 per pound, jelly beans cost $2.00 per pound, and hard candy costs $2.60 per pound. The mixture calls for three times as many gummy candy pieces as jelly beans. The total cost of the mixture is $21.80. How much of each ingredient did the store use?

Answer 1

Answer:

Store used 7.5 pounds of gummy candy, 2.5 pounds of jelly beans, and 3 pounds of hard candy.

Step-by-step explanation:

Let the amount of gummy candy be 'x'.

Let the amount of jelly beans be 'y'.

Let the amount of hard candy 'z'.

Now Given:

Sue is buying 13 pound of mixture.

So we can say that;

$x+y+z =13$

But Given:

The mixture calls for three times as many gummy candy pieces as jelly beans.

$x=3y$

Substituting the value of x in above equation we get;

$3y+y+z=13\\\\4y +z =13 \ \ \ \ \ equation \ 1$

Also Given:

cost of gummy candy = $1.20

cost of jelly beans = $2.00

cost of hard candy = $2.60

Total Cost of mixture  = $21.80

Now Total Cost of mixture is equal to cost of gummy candy multiplied amount of gummy candy plus cost of jelly bean multiplied amount of jelly bean plus cost of hard candy multiplied amount of hard candy.

framing in equation form we get;

$1.2x+2y+2.6z=21.80$

But  $x=3y$

So $1.2(3y)+2y+2.6z=21.80\\\\3.6y+2y+2.6z=21.80\\\\5.6y+2.6z=21.80$

Now Multiplying by both side by 10 we get;

$10(5.6y+2.6z)=21.80\times 10\\\\10\times5.6y + 10\times2.6z =218\\\\56y+26z=218 \ \ \ \ \ equation \ 2$

Now Multiplying equation 1 by 14 we get;

$14(4y +z) =13\times14\\\\14\times4y +14z =182\\\\56y+14z=182$

Now Subtracting equation 3 from equation 2 we get;

$(56y+26z) - (56y+14z) =218-182\\\\56y +26z-56y-14z=36\\\\12z=36\\\\z=\frac{36}{12} = 3 \ pounds$

Now Substituting value of z in equation 1 we get;

$4y+z=13\\\\4y+3=13\\\\4y=13-3\\\\4y = 10\\\\y=\frac{10}{4} = 2.5 \ pounds$

Now also;

$x= 3y\\\\x =3\times2.5 =7.5 \ pounds$

Hence Store used 7.5 pounds of gummy candy, 2.5 pounds of jelly beans, and 3 pounds of hard candy.