Question

A store allows customers to fill their own bags of candy. Terri decides she only wants jelly beans and chocolate drops. Jelly beans sell for $0.90 per pound, and chocolate drops sell for $0.70 per pound. Terri’s bag weighs 5 pounds and it costs $4.10.

a. 2 pounds of jellybeans; 3 pounds of chocolate drops

b. 4 pounds of jellybeans; 1 pound of chocolate drops

c. 1 pound of jellybeans; 4 pounds of chocolate drops

d. 3 pounds of jellybeans; 2 pounds of chocolate drops

Answer 1

Option D is correct that she took 3 pounds of jellybeans and 2 pounds of chocolate drops

Explanation:

Given :

Terri wants jelly beans and chocolate drops.

Jelly beans sell for $0.90 per pound

Chocolate drops sell for $0.70 per pound.

Terri’s bag weighs 5 pounds

It costs $4.10.

To Find : How much she bought jellybeans and chocolate drops?

Solution :

Let she took x pounds of jellybeans.

Let she took y pounds of chocolate drops.

Since we are given that her bag weighs 5 pounds .

⇒
`x+y=5` ---(A)

Now cost of 1 pound of jelly beans = $0.90

So, Cost of x pounds of jellybeans. = $0.90 x

Now cost of 1 pound of chocolate drops. =$0.70

So, Cost of y pounds of chocolate drops. = $0.70 y

Since we are given that total cost of her bag of 5 pounds is $4.10

⇒
`0.90 x+0.70 y= 4.10` ---(B)

Solving A and B by using substitution method

Substitute value of x from (A) in (B)

⇒
`0.90 (5-y)+0.70 y= 4.10`

⇒
`4.5-0.90 y+0.70 y= 4.10`

⇒
`4.5-0.20 y= 4.10`

⇒
`4.5-4.10= 0.20 y`

⇒
`0.4= 0.20 y`

⇒
`(0.4)/(0.20) =y`

⇒
`2 =y`

Thus, she took y = 2 pounds of chocolate drops.

Now to calculate x substitute this value of y in (A)

⇒
`x+2=5`

⇒
`x=5-2`

⇒
`x=3`

Thus, she took x = 3 pounds of jellybeans

Hence , Option D is correct that she took 3 pounds of jellybeans and 2 pounds of chocolate drops