The number of marbles Marci has is 2/3 the number Tanya has. Together they have 40 marbles. How many marbles does Tanya have?
x + (2/3)x = 40
x = 40/(1 2/3)
x = 24
Let's assume the number of marbles Tanya has as x.
Given that the number of marbles Marci has is 2/3 of Tanya's, we can say Marci has (2/3)x marbles.
Together they have 40 marbles, so we can write the equation:
x + (2/3)x = 40
To combine the x's, we need a common denominator. The least common multiple (LCM) of 1 and 3 is 3, so we can write:
(3/3)x + (2/3)x = 40
Combining the x's, we get:
(5/3)x = 40
To solve for x, we can multiply both sides of the equation by the reciprocal of (5/3), which is (3/5):
(3/5) * (5/3)x = (3/5) * 40
The (5/3)'s cancel out on the left side, simplifying the equation to:
x = (3/5) * 40
Multiplying (3/5) by 40, we get:
x = 24
Therefore, Tanya has 24 marbles.
To find out how many marbles Tanya has, we can set up an equation based on the given information. Let's say the number of marbles Tanya has is x.
According to the problem, Marci has 2/3 the number of marbles Tanya has. So, the number of marbles Marci has is (2/3) * x.
Together, Marci and Tanya have a total of 40 marbles. We can write this information as an equation:
x + (2/3)x = 40
To solve this equation, we need to combine like terms:
(1 + 2/3)x = 40
To simplify the equation, we can convert the fraction 2/3 into a decimal:
(1 + 0.67)x = 40
1.67x = 40
Now we can solve for x by dividing both sides of the equation by 1.67:
x = 40 / 1.67
Using a calculator, we find that x is approximately 23.95.
Therefore, Tanya has approximately 23.95 marbles. Since we can't have a fraction of a marble, we can conclude that Tanya has 24 marbles.