Question

Alexandra bought 4 hamburgers and 3 drinks for her family. The cost was $18.25. Tyler bought 6 hamburgers and 4 drinks at the same fast food restaurant for $26.50. What is the total cost of one hamburger and one drink?

A. $1.75
B. $2.65
C. $3.25
D. $5.00

(Please also explain how you did it as well.)

Answer 1

x= hamburger
y=drink

we want to get the value of one variable to find the value of the other

tyler: 6x+4y=26.50
alexandra: 4x+3y=18.25

subtracting tyler from alex ⇒ 2x+y=8.25

multiply this by 2 ⇒ 2(2x+y=8.25) ⇒ [4x+2y=16.50]

now, subtract alex from this to isolate y ⇒ 4x+3y=18.25
- [4x+2y=16.50]

⇒ y=1.75

now plug in to any of the previous equations and solve for x:

4x+3(1.75)=18.25
4x+5.25=18.25
-5.25 -5.25

4x=13 ⇒ x=3.25
/4 /4

6(3.25)+4(1.75)=26.50
4(3.25)+3(1.75)=18.25

hamburger costs 3.25 and drink costs 1.75
hamburger and drink will cost 5.00

Answer 2

3(4h+3d=18.25)-2(6h+4d=26.50)

12h+9d-12h-8d=54.75-53

d=1.75, use either original equation to solve for h...

4h+3(1.75)=18.25

4h+5.25=18.25

4h=13

h=3.25

So the cost of one hamburger and one drink is:

3.25+1.75=$5.00