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

( also explain how you did it as well.)

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

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

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