Ali is x years old and her sister Sara is (10x - 24) years old. Given that Sara is twice as old as Ali, what is Sara’s age?

The key to solving this problem is realizing that you are looking for the number of whole, 5 × 5 cm squares that can be cut from this paper. There will be paper leftover, since the dimensions of the paper are not exactly divisible by 5 cm.
There will be only 7 rows of squares possible along the 38 - cm side, because 38 ÷ 5 = 7/6. This is rounded to 7 because the .6 would only provide a 3 cm side and we need 5 cm sides. The 3 cm would be a leftover scrap, not useful for cutting another square.
(Note: The normal rounding process is different for problems like this. Normally, you would round 7.6 to 8. However, since the decimal value here is unusable, you just discard it when rounding and round down instead.)
Similarly, there will be only 10 columns of squares possible along the 52-cm side, because 52 ÷ 5 = 10.4 or 10. (The extra 2 cm is also not enough for a square side.) 10 × 7 = 70 whole, 5 × 5 cm squares

Step 1:
This month Jane walked a fraction of the distance she walked last month, 36 miles is part of a whole. To get the whole, you first have to turn the percentage into a decimal.
90% = 90/100
=0.9
Step 2:
We then divide the part by the decimal in the last step to get the whole.
36/0.9= 40.
As a way of checking, you can divide 36 by 40 and take note of the decimal you get.
36/40 = 0.9, which tells us that our answer is correct.
Jane walked 40 miles last month.

Step 1:
We first have to read the fraction correctly according to the decimal place value. The decimal 0.62 is sixty-two hundredths.
Step 2:
We create a fraction from how the decimal is read. The fraction for sixty-two hundredths is 62/100.
Step 3:
Since we do not see 62/100 as an answer choice it means we must simplify our fraction. We then have to divide both the numerator and denominator of 62/100 by the same number until we get to a fraction in its simplest form. Since both numbers are even, we will first divide both the numerator and denominator by 2.
\(\frac{\mathrm{62} }{\mathrm{100}}\) = \(\frac{\mathrm{62\div2} }{\mathrm{100\div2}}\)
= \(\frac{\mathrm{31} }{\mathrm{50}}\)
0.62 is \(\frac{\mathrm{31} }{\mathrm{50}}\) as a fraction in its simplest form.

There are 18 total pieces of candy and 3 lollipops. Therefore, the probability of picking one lollipop is 3/18 which simplifies to 1/6.

The first step is to subtract (resulting in −1.88); then add the result to 14.2 (making 12.32 the solution). Line up decimal points when adding or subtracting.

Multiply the area by the charge per square foot.
Area = 50 × 30 = 1,500 square feet
1,500 × 0.05 = $75.00

We will first eliminate the parenthesis from the equation by using the distributive law. We will then isolate the variable on the left-hand side by carrying out the necessary mathematical operations on both sides of the equation. Finally, we will simplify the numbers to solve the equation for y.
Step 1:
Eliminate the parenthesis
We will apply the distributive law by multiplying both the terms in parenthesis by 6. This will eliminate the parenthesis from the equation.
6 × y + 6 × 3 = 48
Or, 6y + 18 = 48
Step 2:
Isolate the variable
We will first subtract 18 from both sides of the equation and carry out the subtraction.
6y + 18 – 18 = 48 – 18
Or, 6y = 30
We will then divide both sides of the equation by 6 to isolate y on the left-hand side, before simplifying the numbers to solve the equation.
(6y)/6 = 30/6
Or, y = 5

When estimating, we are trying to find a value that is close to the answer but doesn’t have to be exact. We round each number and then solve, which is how we arrive at our estimate of the answer.
When estimating, we are trying to find a value that is close to the answer, but doesn’t have to be exact. We round each number and then solve, which is how we arrive at our estimate of the answer.
Rounding is when we make a number “simpler” but keep the value as close to the original number as possible. To round a number:
Determine which digit or place (value) is the number you want to “round to.” All numbers after this (to the right) will become zeroes after rounding.
Keep it the same number if the next number (the number to its right) is less than 5. Then, change all other numbers to the right to 0. For example, 132 rounded to the nearest ten would be 130. (132 is closer to 130 than it is to 140.)
Increase the number by 1 if the next number (the number to its right) is 5 or more. Then, change all other numbers to the right to 0. For example, 158 rounded to the nearest hundred would be 200. (158 is closer to 200 than it is to 100.)
In order to get close to the actual answer, round each number to the second largest place value.
For example:
325.13 → 330
25 → 30
5.7 → 6
5.78 → 5.8
For this problem:
0.289 → 0.3
3.4 → 3
Then we continue with the problem. In this case, we are dividing the carafe (3 liters) by the number of cups (0.3 liters):
3 ÷ 0.3 = 10 cups*
*If you do not have access to a calculator for this question, you may solve the final step like this:
Convert the decimal into a fraction (it reads, “three tenths” so you can simply write that out at a fraction):
3 ÷ 3/10 =
When dividing a whole number by a fraction, first convert the whole number into a fraction by making the whole number the numerator and 1 the denominator.
3/1 ÷ 3/10 =
Then, because you are dividing by a fraction, flip the second fraction and multiply.
3/1 • 10/3 =
You can cross reduce the 3’s by dividing both by 3. (Or you can multiply the two fractions as they are and reduce the answer.)
3÷3/1 • 10/3÷3 = 1/1 • 10/1 = 10

Step 1: Translate Given Information into Algebra Expression
For this question, we are looking to write an expression to represent a certain total. The starting amount will be an unknown amount and every other amount will be written in terms of the initial amount.
In the given prompt, we know that Orlando drove an unknown number of miles during his first week, so the number of miles he drove that week will be assigned a variable (x).
Number of miles driven first week → x
We are also given that Orlando drove fifteen more miles in his second week in comparison to the number he drove the first week. This means,
Number of miles driven second week → x + 15
Finally, we are told that he drove twenty-five fewer miles in his third week when compared to the first week. Since he drove fewer miles, this means we will be subtracting 25 miles from the amount he drove the first week which is represented by x.
Number of miles driven third week → x – 25
Step 2: Determine Total
Now that we have all individual expressions, we can find the final sum.
We are asked to write an expression that represents the total number of miles that Orlando drove in the 3-week road trip. To find the total, we need to find the expression that adds all expressions and simplify.
x+ x + 15 + x – 25
We can now rearrange the expression to group like terms together. Remember to include the sign IN FRONT of a term.
x + x + 15 + x – 25
Now becomes:
x + x + x + 15 – 25
The expression becomes::
3x – 10

Step 1: Calculate Part (Non-100%)
In reading the prompt, the first step is to identify the amounts needed to be added to calculate the portion of the budget that has already been spent, which represents the part (non-100%).
75 + 65 = 140
Making 140 the part (non-100%).
Step 2: Divide the Part (Non-100%) by the Whole (100%)
In order to find the percentage, we have to divide the part of the total available amount by the total amount available. In this case, the non-100% part that we have, 140, will be divided by the total amount available that represents 100%, which is 680.
140÷ 680 = 0.2058823529
We can round this off to the third-place value. Check your answer choices to see if numbers were rounded to a different place value.
So let’s look at the third place value:
0.2058823529
We look to the right and see an 8. Since an 8 is 5 or more, that means the underlined digit goes up by one so the 5 becomes a 6.
0.206
Every other number to the right of the 5 would turn to 0, and since they would have no value, we can get rid of them.
Step 3: Multiply by 100
Now that we have our decimal, we have to turn it into a percent. Remember, we turn a decimal into a percent by multiplying it by 100, which is the same as moving the decimal point two spots to the right.
0.206 × 100 = 20.6%
This tells us how much of the budget has already been spent. Finally, we have to find the percentage of what she has left.
Step 4: Subtract Budget Spent from Total Budget
The event coordinator spent 20.6% of her budget. In order to find the percentage that is left we will subtract the percentage she spent from 100%.
100% – 20.6% = 79.4%
The event coordinator has 79.4% of her budget left.