We can write this as an equation:

\(\displaystyle 0.70\cdot x=35\)

\(\displaystyle x=\frac{35}{0.7}\)

\(\displaystyle x=50\)

\(\displaystyle \frac{80}{100}=\frac{4}{5}\)

\(\displaystyle \frac{4}{5}x=72\)

Divide by fractions:

  \(\displaystyle x=\frac{5}{4}\cdot 72=90\)

If $300 was 15% of Malcolm's money, then we can figure out how much money Malcolm had by creating this equation:

\(\displaystyle .15x=300\)

In this case, Malcolm had $2,000. Since he spent $300 of it on a bicycle, he has only $1,700 left.

The key to this problem is identifying that "15% of \(\displaystyle x\)" is the same as \(\displaystyle 0.15x\). With this information, we can write out the simple equation

\(\displaystyle 45=0.15x\)

Dividing both sides by \(\displaystyle 0.15\) gives us

\(\displaystyle x=300\)

\(\displaystyle 1\tfrac{1}{2}\) % of a number, or, equivalently, 1.5% of a number, is the same as 0.015 multiplied by that number. If we call that number \(\displaystyle x\), then 

\(\displaystyle 0.015x=900\)

\(\displaystyle x = 900\div 0.015 = 60,000\)

We know that prior to her purchase, $900 was 24% of Dana's Savings. Therefore, Dana's total savings prior to her purchase can be modeled as \(\displaystyle 0.24x=900\), where \(\displaystyle x\) is Dana's total savings. Solving for \(\displaystyle x\) would give you \(\displaystyle x=3750\), which indicates that Dana's savings was $3750 prior to her purchase. After her purchase, she will have $2850 left.

If \(\displaystyle x\) is the total number of marbles in the bag, then \(\displaystyle 0.24x=36\), since 24% of marbles in the bag are blue and there are 36 marbles. Solving for this equation will give you \(\displaystyle x=150\), which means there must be a total of 150 marbles in the bag.

From the given information here, we know that 12% of the total number equals 27. Mathematically, if we use \(\displaystyle x\) to represent the total that we are looking for, we can write this as 

\(\displaystyle (0.12)(x)=27\)

The next step is dividing both sides by \(\displaystyle 0.12\).

\(\displaystyle \frac{27}{0.12}=225\)

so there are 225 students in the school.

To figure out the value, translate the question into an equation, knowing that "is" means equals, and "of" means multiply:

\(\displaystyle \small 4 = 48\%*x\)

To solve, turn the percentage into a decimal:

\(\displaystyle \small 4=0.48*x\) now divide both sides by 0.48

\(\displaystyle \small 8.\overline{3}=x\)

To determine the whole, translate the question into an equation, knowing that "is" means equals and "of" means multiply:

\(\displaystyle \small 10 = 180\%*x\) convert the percentage into a decimal:

\(\displaystyle \small 10 = 1.8*x\) divide both sides by 1.8

\(\displaystyle \small 5.\overline{5}=x\)