Directions solve each of the following problems. Besure to show the equation used for the solution.
In a town election, the winning candidate had 220 more votes than the loser. If 810 votes were cast in all, how many votes did each candidate received?
answer:
Let x = the number of votes received by the losing candidate, then the winning candidate received x + 220 votes. The sum of these two amounts equal 810.
Equation:
X+(x +200)=180 simplify & solve for x.
2x+220=810 subtract 220 from both sides.
2x = 590 divide both sides by 2
X = 295
The losing candidate received 295 votes.
The winning candidate received 295 + 220 = 515 votes.
correct. You can generally check these your self by going back to the original problem statement.
total= one candidate + other candidate
= 295 + 295 + 220 = 810
To solve this problem:
1. Let x represent the number of votes received by the losing candidate.
2. Since the winning candidate had 220 more votes, the number of votes they received would be x + 220.
3. The sum of the votes received by both candidates should equal the total number of votes cast, which is 810.
4. Write the equation to represent this situation: x + (x + 220) = 810.
5. Simplify the equation: 2x + 220 = 810.
6. To isolate x, subtract 220 from both sides of the equation: 2x = 810 - 220.
7. Simplify further: 2x = 590.
8. Divide both sides of the equation by 2 to solve for x: x = 590 / 2.
9. Calculate x: x = 295. This means the losing candidate received 295 votes.
10. To find the number of votes received by the winning candidate, add 220 to x: 295 + 220 = 515. The winning candidate received 515 votes.
To double-check your solution, you can verify that the total number of votes is equal to the sum of votes received by both candidates. In this case, 295 + 515 + 220 = 810, confirming the accuracy of the solution.