Question

Raul bought a soft drink and a sandwich for $9.90. What is the price of each if the sandwich cost 3.5 times as much as the soft drink?

A) Sandwich costs $5.94 and the soda costs $3.96
B) Sandwich costs $7.70 and the soda costs $2.20
C) Sandwich costs $5.40 and the soda costs $4.50
D) Sandwich costs $2.83 and the soda costs $9.90

Answer 1

you would need to create 2 equations first, the variables I am using are X=price for a sandwich and Y=Soft Drink

the first equation is going to be total price so you add x and y

X+Y=9.90

next, you need to create another equation to be able to get the price

3.5Y=X

next substitute X in the first equation with the second

(3.5Y)+Y=9.90

add

4.5Y=9.90

and now divide each side by 4.5

Y=$2.20

now substitute the Y in the first equation with it's value

X+(2.20)=9.90

now take away 2.20 from each side to get X

X=$7.70

so the answer is B

Answer 2

First create a ratio:

The sandwich cost 3.5 more than the drink therefore the ratio is 3.5:1

Then add the two sides of the ratio together to get the total parts of the ratio
3.5+1 = 4.5

Now that we know the total parts of the ratio we can solve for one part by dividing the total cost $9.90 by the total parts of the ratio 4.5+

$9.90/4.5 = 2.20

Since we know that each part of the ratio is 2.20 we multiply both sides of the ratio by 2.20

3.5 *2.20 = 7.70
1 * 2.20 = 2.20

Therefore the answer is B