Alyssa, Bert, and Cara are running for school president. Alyssa receives two-sevenths of the votes. Bert receives sixty-five percent of the remaining votes, and the rest of the votes go to Cara. If Cara receives 315 votes, how many votes were there in all?
Please help with step by step.
number of votes --- x
Alyssa gets (2/7)x
leaving 5x/7
Bert gets 65% of that or .65(5x/7)
Cara gets x - 2x/7 - .65(5x/7)
but that is 315
x - 2x/7 - .65(5x/7) = 315
times 7
7x - 2x - .65(5x) = 315
1.75x = 2205
x = 1260 ----> number of votes
check:
Alyssa gets (2/7)1260 = 360
leaving 900 votes
Bert gets 65% of 900 = 585
Carla gets 1260 - 360 - 585 = 315
All is good!
idk the answer
. Alyssa receives two-sevenths of the votes. Bert receives sixty-five percent of the remaining votes, and the rest of the votes go to Cara. If Cara receives 315 votes, how many votes were there in all?
480
21
Alyssa, Bert, and Cara are running for school president. Alyssa receives one-third of the votes. Bert receives 60 percent of the remaining votes, and the rest of the votes go to Cara. If Cara receives 96 votes, how many votes were there in all?
967
its 360 ;)
To find the total number of votes, we need to calculate the votes received by Alyssa and Bert, and then add them to Cara's votes.
Step 1: Find Alyssa's votes
Since Alyssa receives two-sevenths of the total votes, we need to determine what fraction of the total votes Cara received. Let's call the total number of votes "x".
So, Alyssa receives (2/7) * x votes.
Step 2: Find Bert's votes
Bert receives sixty-five percent of the remaining votes, after Alyssa's votes are deducted. To calculate Bert's votes, we need to subtract the votes received by Alyssa from the total votes "x" and multiply the remaining votes by 65%.
Remaining votes = Total votes - Alyssa's votes
Remaining votes = x - (2/7) * x
Bert's votes = 65% * Remaining votes
Bert's votes = 0.65 * (x - (2/7) * x)
Step 3: Find the total number of votes
The total number of votes is the sum of Alyssa's votes, Bert's votes, and Cara's votes.
Total votes = Alyssa's votes + Bert's votes + Cara's votes
Total votes = (2/7) * x + 0.65 * (x - (2/7) * x) + 315
Now, we can solve the equation to find the value of "x".
Let's simplify the equation:
Total votes = (2/7) * x + 0.65 * (x - (2/7) * x) + 315
Total votes = (2/7) * x + 0.65 * (5/7) * x + 315
Total votes = (2/7) * x + (13/20) * x + 315
Total votes = (26/70) * x + (13/20) * x + 315
Total votes = (33/70) * x + 315
Now, we have an equation to solve for "x". Unfortunately, there's not enough information to determine the exact value of "x".