2)3/14 of the rosebuds in a garden bloomed yesterday, and 2/5 of the remaining rosebuds bloomed today. 66 rosebuds have not yet bloomed.
1. How many rosebuds were there in total?
2.How many rosebuds bloomed today?
plz help, i don't kno y but i forgot how to do these problems
Let R be the total rosebuds.
Rosebuds bloomed= rosebouds-notbloomed
3/14 * R+ 2/5(11/14)R = R-66
Let N be the total number of rosebuds in the beginning. Turn the word statement into an equation.
(3/14) N + (2/5)(11/14)N + 66 = N
Now solve for N
(15/70 + 22/70)N + 66 = N
(33/70)N = 66
N = 140
Today, 22/70 of that number bloomed.
thx it helped a lot
To solve these problems, we need to break down the information given step by step.
1. How many rosebuds were there in total?
First, we know that 2/3 of the rosebuds in the garden bloomed yesterday. Let's call the total number of rosebuds x. Therefore, 2/3 of x = (2/3)*x rosebuds bloomed yesterday.
Next, it says that 2/5 of the remaining rosebuds bloomed today. After yesterday, there were (x - 2/3x) rosebuds left. So, 2/5 of (x - 2/3x) bloomed today.
We can now write an equation to represent the total number of rosebuds:
(x - 2/3x) - 2/5(x - 2/3x) = 66
To solve this equation, we can simplify it step by step:
1. Multiply the denominators and get rid of their respective denominators:
(5(x - 2/3x) - 2(x - 2/3x)) = 66
2. Simplify the equation further:
(5x - 10/3x) - (2x - 4/3x) = 66
3. Combine like terms:
(15x - 20 - 6x + 4) / 3 = 66
(9x - 16) / 3 = 66
4. Multiply both sides of the equation by 3:
9x - 16 = 198
5. Add 16 to both sides of the equation:
9x = 214
6. Divide both sides of the equation by 9:
x = 23.77
Since the number of rosebuds must be a whole number, we round the result to the nearest whole number:
Total number of rosebuds in the garden = 24
Therefore, there were 24 rosebuds in total.
2. How many rosebuds bloomed today?
We know that 2/5 of the remaining rosebuds bloomed today, and we have already found that the total number of rosebuds is 24. So, we can calculate the number of rosebuds that bloomed today as follows:
Number of rosebuds that bloomed today = 2/5 * (24 - 2/3 * 24)
Simplifying:
Number of rosebuds that bloomed today = 2/5 * (24 - 16)
Number of rosebuds that bloomed today = 2/5 * 8
Number of rosebuds that bloomed today = 16/5
Using division, we can write:
Number of rosebuds that bloomed today = 3 rest 1
Therefore, 16 rosebuds bloomed today.