Marnie collects red, blue and purple buttons. At the beginning of the year she has 360 buttons in a box. The ratio of red buttons to blue buttons is 4:3 and there are twice as many red buttons as purple buttons.
a.What is the ratio of blue buttons to purple buttons at the beginning of the year?
b.After Marnie adds another 200 buttons –some red and some blue – at the end of the year, the number of red buttons increased by 75% and the number of blue buttons increased by two-thirds.
i.What is the new ratio of red buttons to blue buttons?
ii.Express the number of purple buttons as a fraction of the new total number of buttons.
iii.Express the number of blue buttons as a percentage of the number of red buttons. (Round to one decimal place).
red-blue-purple = 4-3-2. red =160; blue = 120; purple -= 80.
New total 560. Red has increased from 160 to (add 75% = 120) 280. Extra blue is 200 - 120 = 80. Total blue = 120 + 80 = 200.
Blue as percentage of red = (200/280)x100 = 71.4%
Ali has 40 red buttons,60 green buttons,and 5 blue buttons
To solve this problem, we'll break it down step by step.
a. To find the ratio of blue buttons to purple buttons, we need to determine the number of blue and purple buttons separately. Let's use the information given.
Let the number of red buttons be represented by the variable 'r'.
Then the number of blue buttons would be (3/7)r (since the ratio of red to blue buttons is 4:3).
And the number of purple buttons would be (1/2)r (since there are twice as many red buttons as purple buttons).
To find the total number of buttons, we can add these quantities together:
r + (3/7)r + (1/2)r = 360
We can simplify this equation by finding a common denominator for the fractions:
(14/14)r + (6/14)r + (7/14)r = 360
(27/14)r = 360
Now we can solve for 'r' by multiplying both sides by (14/27):
r = (360 * 14) / 27
We find that r ≈ 187.41, which represents the number of red buttons.
The number of blue buttons is (3/7) * 187.41 ≈ 80.29
The number of purple buttons is (1/2) * 187.41 ≈ 93.71
Therefore, the ratio of blue buttons to purple buttons at the beginning of the year is approximately 80.29:93.71, or simplified, 40.15:46.86.
b. Now let's tackle the second part.
i. To find the new ratio of red buttons to blue buttons, we need to calculate the increase in the number of red and blue buttons.
The number of red buttons increased by 75%, which means it became 1.75 times its original value:
New number of red buttons = 1.75 * 187.41
The number of blue buttons increased by two-thirds, which means it became 1 + (2/3) times its original value:
New number of blue buttons = (1 + (2/3)) * 80.29
Now we can calculate the new ratio of red buttons to blue buttons:
(1.75 * 187.41) : ((1 + (2/3)) * 80.29)
ii. To express the number of purple buttons as a fraction of the new total number of buttons, we add the new number of red and blue buttons, along with the initial number of purple buttons:
(1.75 * 187.41) + ((1 + (2/3)) * 80.29) + 93.71
Then we express the number of purple buttons as a fraction of this sum:
93.71 / ((1.75 * 187.41) + ((1 + (2/3)) * 80.29) + 93.71)
iii. Finally, to express the number of blue buttons as a percentage of the number of red buttons, we divide the number of blue buttons by the number of red buttons:
(1 + (2/3)) * 80.29 / (1.75 * 187.41) * 100
After substituting the values into the respective equations, you'll arrive at the final answers.