There are 39 purple marbles in the bag
Step-by-step explanation:
The given is:
- There are 55 purple and green marbles in total in a bage
- The number of purple marbles is 7 more than 2 times the number of green marbles
We need to find how many purple marbles in the bag
Assume that the number of the purple marbles is P and the number
of the green marbles is G
∵ There are P purple marbles and G green marbles in the bag
∵ There are 55 marbles in the bag
∴ P + G = 55 ⇒ (1)
∵ The number of purple marbles is 7 more than 2 times the number
of green marbles
- Add 7 and 2 times G to get P
∴ P = 7 + 2 G
- Subtract 2 G from both sides
∴ P - 2 G = 7 ⇒ (2)
Let us solve the system of equations to find P
Multiply equation (1) by 2 to eliminate G
∵ 2 P + 2 G = 110 ⇒ (3)
- Add equations (2) and (3)
∴ 3 P = 117
- Divide both sides by 3
∴ P = 39
∵ P represents the number of the purple marbles in the bag
∴ There are 39 purple marbles in the bag
There are 39 purple marbles in the bag
Learn more:
You can learn more about the system of equations in brainly.com/question/3739260
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