Answer:
The system of equations is :
6 p + 4 d = 34
12 p + 7 d = 66.25
The price of a drink is $1.75
Explanation:
Assume that the price of one bag of popcorn is $p and the price of a drink is $d
∵ Samuel spends a total of $34 on 6 bags of popcorn and
4 drinks
- Multiply p by 6 and d by 4, then add the products and equate
the sum by 34
∴ 6 p + 4 d = 34 ⇒ (1)
∵ Christopher spends a total of $66.25 on 12 bags of popcorn
and 7 drinks
- Multiply p by 12 and d by 7, then add the products and equate
the sum by 66.25
∴ 12 p + 7 d = 66.25 ⇒ (2)
The system of equations is :
6 p + 4 d = 34
12 p + 7 d = 66.25
Now let us solve it
Multiply equation (1) by -2 to make the coefficients of p in the two equations equal in values and opposite in signs to eliminate it
∵ -12 p - 8 d = - 68 ⇒ (3)
- Add equations (2) and (3)
∴ - d = - 1.75
- Divide both sides by -1
∴ d = 1.75
The price of a drink is $1.75