Math Problem PLZ HELP

Question

Tessa did 3/5 of her homework problems on Saturday. On Sunday, she did 1/3 of what was left plus the last 4 problems. How many problems did Tessa do over the weekend?

Answer 1

Tessa did her homework in 3 parts:

1. 3/5 of her total problems
2. 1/3 of her remaining problems
3. the final 4 problems.

Because we are trying to figure out the total number of problems, let's work backwards from the last step (part 3), because this step gives us an actual number of problems to use as a baseline.

Let's represent Tessa's last 4 problems as 4 x's: x x x x

Before completing these 4 problems, Tessa did 1/3 of her remaining problems. This means the final 4 problems were 2/3 of her remaining problems. If we represent the total number of remaining problems as y, we can write this equation: 2/3 * y = 4, where y = 6. Therefore, 1/3 * 6 = 2

Let's visualize the problems Tessa has done so far, with y representing the problems she solved in part 2:

y y x x x x

This is a total of 6 problems.

Now, we finish with part 1 (Tessa did 3/5 of her total problems). If Tessa completed 3/5 of her total problems, the remaining 6 problems from part 2 and part 3 are equal to 2/5 of her total problems. Let's represent the total number of problems as z, and write this equation: 2/5 * z = 6, where z = 15. Therefore, 3/5 * 15 = 9

Let's visualize this to see if it makes sense, with z representing the problems Tessa solved in part 1:

z z z z z z z z z y y x x x x

This is a total of 15 problems.

Part 1: z = 9, which is 3/5 of 15, leaving 6 problems unsolved

Part 2: y = 2, which is 1/3 of 6, leaving 4 problems unsolved

Part 3: x = 4, leaving 0 problems unsolved, so Tessa has finished her homework!

Mathematically and logically this makes sense, so we know that Tessa has done 15 problems total over the weekend!

Answer 2

To find how many problems she did, you need to add 3/5, 1/3, and 4. First you need to find the least common denominator of all three numbers and then rewrite the numbers using the least common denominator:

Least common denominator is 15, so:

3/5 --> 9/15 , 1/3 --> 5/15 , and 4 --> 60/15

Now you can add all the fractions together:

9/15 + 5/15 + 60/15 = 74/15

Then that your answer and simplify.

74/15 --> 4 14/15. So she did 4 14/15 problems, or 5 problems when the answer is rounded to the nearest whole number.