There are 750 (2 kg) bags and 350 (4 kg) bags in the shipment
Step-by-step explanation:
The given is:
- A supermarket sells 2 kg and 4 kg of sugar a shipment of 1100 bags of sugar
- The total mass of the sugar is 2900 kg
We need to find how many 2 kg bags and 4 kg bags are in the shipment
Assume that x represents the number of 2 kg bags and y represents the number of 4 kg bags
∵ x is the number of 2 kg bags
∵ y is the number of 4 kg bags
∵ The total number of bags are 1100
- Add x and y, then equate the sum by 1100
∴ x + y = 1100 ⇒ (1)
∵ The total mass of sugar is 2900 kg
- Multiply x by 2 and y by 4 to find the mass of the bags, then
add the two product and equate them by 2900
∴ 2x + 4y = 2900 ⇒ (2)
Now we have a system of equations to solve it
Multiply equation (1) by -2 to eliminate x
∴ -2x - 2y = -2200 ⇒ (3)
- Add equations (2) and (3)
∴ 2y = 700
- Divide both sides by 2
∴ y = 350
- Substitute the value of y in equation (1) to find x
∵ x + 350 = 1100
- Subtract 350 from both sides
∴ x = 750
There are 750 (2 kg) bags and 350 (4 kg) bags in the shipment
Learn more:
You can learn more about the system of equations in brainly.com/question/6075514
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