Final answer:
Joshua initially has 210 ribbons in total. To find this, the math problem involved calculating the total by evaluating the given fractions of colored ribbons and solving for the unknown total number of ribbons, x. The correct answer is option B) 210 ribbons.
Step-by-step explanation:
To solve the problem given, we need to figure out how many ribbons Joshua initially has, given that we know the number of yellow ribbons and the proportions of the other colors.
Let's represent the total number of ribbons by x. According to the problem, 1/4 of the ribbons are blue, so the remainder, which would be (1 - 1/4)x or 3/4x, are not blue. Of this remainder, 2/5 are red ribbons. Therefore, (2/5) * (3/4)x ribbons are red.
The rest of the ribbons, which are yellow, number 63. This can be represented as:
x - (1/4)x - (2/5)*(3/4)x = 63
Simplifying the expression gives:
3/4x - (2/5)*(3/4)x = 63
3/4x - (3/5)*(3/4)x = 63
3/4x - 9/20x = 63
To find a common denominator, we can convert 3/4 into 15/20, which gives us:
15/20x - 9/20x = 63
This simplifies to 6/20x or 3/10x = 63
Multiplying both sides of the equation by 10/3 gives us:
x = 63 * (10/3)
x = 63 * 10 / 3
x = 210 / 3
x = 70
Therefore, Joshua initially has 70 ribbons of each color, and since we're counting all of them, the total is:
x * 3 = 70 * 3
x = 210
So the correct answer is:
B) 210 ribbons