To find the discounted amount, convert the percent to a decimal and multiply it by the original cost.

\(\displaystyle 25\%=0.25\)

\(\displaystyle \$60*0.25=\$15\)

Then, subtract the discount amount from the original cost.

\(\displaystyle \$60-\$15=\$45\)

Answer: \(\displaystyle \$45\)

40% of the voters were registered as independents, so 60% were registered as a member of a political party. Since 60% of the voters numbered 15,934, we can find the total number of voters by setting up and solving a proportion:

\(\displaystyle \frac{60}{100} = \frac{15,934}{N}\)

\(\displaystyle 60 N = 100 \cdot 15,934\)

\(\displaystyle 60 N = 1,593,400\)

\(\displaystyle 60 N \div 60= 1,593,400 \div 60\)

\(\displaystyle N= 26,556.7\)

which rounds to 26,557 voters.

2% of the voters were registered as members of other parties, and 40% were unaffiliated, so we want to calculate 42% of 17,856, or, equivalently, 

\(\displaystyle 17,856 \times 0.42 = 7,499.52\)

which, to the nearest whole number, rounds to 7,500 voters.

Set up the proportion statement and solve for \(\displaystyle N\):

\(\displaystyle \frac{240}{N}= \frac{30}{100}\)

Cross-multiply:

\(\displaystyle N\cdot 30 = 240\cdot 100 = 24,000\)

\(\displaystyle N\cdot 30 \div 30= 24,000 \div 30\)

\(\displaystyle N=800\)

Set up the proportion statement and solve for \(\displaystyle N\) by cross-multiplying:

\(\displaystyle \frac{420}{N}= \frac{150}{100}\)

\(\displaystyle N \cdot 150 = 420 \cdot 100 = 42,000\)

\(\displaystyle N \cdot 150 \div 150 = 42,000 \div 150\)

\(\displaystyle N = 280\)

Set up the proportion statement and solve for \(\displaystyle N\) by cross-multiplying:

\(\displaystyle \frac{70}{N } = \frac{\frac{1}{5}}{100}\)

\(\displaystyle N \cdot \frac{1}{5}=70 \cdot 100 = 7,000\)

\(\displaystyle N \cdot \frac{1}{5} \cdot 5 = 7,000 \cdot 5\)

\(\displaystyle N= 35,000\)

\(\displaystyle 24=25\%\cdot c\)

Think \(\displaystyle a\) is \(\displaystyle b\%\) of \(\displaystyle c\).

So:

\(\displaystyle 24=a\) and \(\displaystyle 25=b\).

We have:

\(\displaystyle \frac{24}{0.25}=c\Rightarrow c=96\)

Paying at a 15% discount is equvalent to paying 85% of the original price, so $196.57 is 85% of the original (non-employee) price, or, equivalently, 0.85 times that price. If \(\displaystyle N\) is that price, then we can set up and solve the equation:

\(\displaystyle 0.85 N = 196.57\)

\(\displaystyle 0.85 N \div 0.85 = 196.57 \div 0.85\)

\(\displaystyle N= 231.26\)

A non-employee would pay $231.26 for the groceries.

This can be solved using a proportion:

\(\displaystyle \frac{10}{100}=\frac{3}{x}\)

Cross multiply and solve for \(\displaystyle x\):

\(\displaystyle 10x=300\)

\(\displaystyle \frac{10x}{10}=\frac{300}{10}\)

\(\displaystyle x=30\)

When Susan's mother agreed to match her savings plus fifty percent, she agreed to give Susan \(\displaystyle \small 100\)% plus \(\displaystyle \small 50\)%.  

\(\displaystyle \small 100+50=150\)

Before multiplying by the amount Susan saved, we must convert \(\displaystyle \small 150\)% to a decimal by dividing by \(\displaystyle \small 100\).

\(\displaystyle \small 150/100=1.5\)

Now we multiply \(\displaystyle \small 1.5\) time $\(\displaystyle \small 600\).

\(\displaystyle \small 1.5\cdot 600=900\)

Susan's mother owes her $\(\displaystyle \small 900\).