Jack and Jill went to Burger Queen. Jack bought 2 hamburgers and 3 shakes for
$4.21 while Jill bought 3 hamburgers and 2 shakes for $5.24. The cost of 1
hamburger and 1 shake is:
A) $1.03
B) $1.54
C) $1.89
D) $9.45
Write down the facts:
2h+3s = 4.21
3h+2s = 5.24
Now you can solve for h and s, and calculate h+s. Nope, too much work.
Instead, just add the two equations, and you see that
5h+5s = 9.45
So, divide by 5 to get
h+s = 1.89
Well, it seems like Jack and Jill have a case of the fast food math blues! Let's solve this tasty mystery together, shall we?
Let's start by figuring out the cost of Jack's meal. He bought 2 hamburgers for let's say X dollars each and 3 shakes for Y dollars each. So we have:
2X + 3Y = $4.21
Now let's move on to Jill's meal. She bought 3 hamburgers (still at X dollars each) and 2 shakes (Y dollars each). So we have:
3X + 2Y = $5.24
Now we have a tasty little system of equations to solve. To make things easier, let's subtract double the first equation from the second equation:
(3X + 2Y) - 2(2X + 3Y) = $5.24 - 2($4.21)
(3X + 2Y) - (4X + 6Y) = $5.24 - $8.42
- X - 4Y = -$3.18
Now let's multiply the first equation by 4 and subtract it from the second equation:
4(2X + 3Y) - (3X + 2Y) = 4($4.21) - $5.24
8X + 12Y - 3X - 2Y = $16.84 - $5.24
5X + 10Y = $11.60
Okay, now we have a tasty system of equations:
- X - 4Y = -$3.18
5X + 10Y = $11.60
Let's solve this using some fancy math magic. Let's multiply the first equation by 5 and the second equation by -1:
-5X - 20Y = -5($3.18)
-5X - 10Y = -$11.60
Now let's add these two equations together:
(-5X - 20Y) + (-5X - 10Y) = -5($3.18) - $11.60
-10X - 30Y = -$15.90 - $11.60
-10X - 30Y = -$27.50
Oh no, did we make a mistake? It seems we've hit a bit of a snag with our calculations. I fear we may have dropped a shake or a hamburger along the way. Let's retrace our steps and re-evaluate this dilemma.
To find the cost of 1 hamburger and 1 shake, we can set up a system of equations using the given information:
Let's assume the cost of 1 hamburger is "H" and the cost of 1 shake is "S".
From Jack's purchase:
2H + 3S = $4.21 ---> Equation 1
From Jill's purchase:
3H + 2S = $5.24 ---> Equation 2
To solve this system of equations, we can use a method called elimination.
Multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of H match:
6H + 9S = $12.63 ---> Equation 3
6H + 4S = $10.48 ---> Equation 4
Now we can subtract Equation 4 from Equation 3 to eliminate H:
(6H + 9S) - (6H + 4S) = $12.63 - $10.48
5S = $2.15
Divide both sides of the equation by 5 to solve for S:
S = $2.15 / 5
= $0.43
So the cost of 1 shake is $0.43.
Now we can substitute the value of S back into either Equation 1 or 2 to solve for H. Let's use Equation 1:
2H + 3($0.43) = $4.21
2H + $1.29 = $4.21
Subtract $1.29 from both sides of the equation:
2H = $4.21 - $1.29
2H = $2.92
Divide both sides of the equation by 2 to solve for H:
H = $2.92 / 2
= $1.46
So the cost of 1 hamburger is $1.46.
Therefore, the cost of 1 hamburger and 1 shake is $1.46 + $0.43 = $1.89.
The correct answer is C) $1.89.
To find the cost of 1 hamburger and 1 shake, we need to set up a system of equations based on the given information.
Let's assume the cost of 1 hamburger is "h" and the cost of 1 shake is "s".
From the information given, we can set up the following equations:
Equation 1: 2h + 3s = 4.21 (Jack's order)
Equation 2: 3h + 2s = 5.24 (Jill's order)
We can solve this system of equations using elimination or substitution method. In this case, let's use the elimination method.
Multiply Equation 1 by 2 and Equation 2 by 3 to eliminate "s":
Equation 1: 4h + 6s = 8.42
Equation 2: 9h + 6s = 15.72
Now, subtract Equation 1 from Equation 2:
(9h + 6s) - (4h + 6s) = 15.72 - 8.42
5h = 7.30
h = 7.30/5
h = 1.46
So, the cost of 1 hamburger is $1.46.
Substitute the value of h into Equation 1 to find the cost of 1 shake:
2(1.46) + 3s = 4.21
2.92 + 3s = 4.21
3s = 4.21 - 2.92
3s = 1.29
s = 1.29/3
s = 0.43
So, the cost of 1 shake is $0.43.
Therefore, the cost of 1 hamburger and 1 shake is $1.46 + $0.43 = $1.89.
Therefore, the answer is C) $1.89.