Question

13) 3 bags of Brand X dog food and 4 bags of Brand Y dog food costs $18,

while 4 bags of Brand X dog food and 3 bags of Brand Y dog food costs
$17. What is the cost of each bag of Brand X?

Answer 1

Each bag of Brand X dog food costs $2.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's assume the cost of each bag of Brand X dog food is represented by x, and the cost of each bag of Brand Y dog food is represented by y.

From the given information, we can create the following equations:

3x + 4y = 18

4x + 3y = 17

Now, we can solve this system of equations:

1. Multiply the first equation by 4 and the second equation by 3 to eliminate the x variable: 12x + 16y = 72 and 12x + 9y = 51
2. Subtract the second equation from the first equation to eliminate the x variable: 12x + 16y - 12x - 9y = 72 - 51
3. Simplify: 7y = 21
4. Divide both sides by 7: y = 3
5. Substitute the value of y back into either of the original equations to solve for x. Let's use the first equation:
   3x + 4(3) = 18
   3x + 12 = 18
   3x = 6
   x = 2

Therefore, each bag of Brand X dog food costs $2.

Answer 2

the cost of brand x dog food is $2

Step-by-step explanation:

Let brand X dog food be represented as A

Let Brand Y dog food be represented as B

3 bags of Brand X dog food and 4 bags of Brand Y dog food costs $18,

3A+4B=18

4 bags of Brand X dog food and 3 bags of Brand Y dog food costs

$17.

4A+3B= 17

• 3A+4B=18
• 4A+3B= 17

Using Elimination method

Multiply

• 3A+4B=18 by coefficient of B in equ ii (3) = 9A+12B=54

• 4A+3B= 17 by coefficient of B in equ i (4) = 16A+12B=68
• subtract equation i from equation ii, since sign is the same in both equations
• 9A+12B-(16A+12B)= 54-68
• open bracket

• 9A+12B-16A-12B= 54-68= -14
• 9A-16A+12B-12B= -14
• -7A= -14
• divide both sides by -7

A = -14/-7= 2

Since the brand X dog food is represented as A

the cost of brand x dog food is $2