Question

A bag contains purple marbles and green marbles, 55 in total. The number of purple marbles is 7 more than 2 times the number of green marbles. How many purple marbles are there?

Answer 1

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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