Question

Consider a survey involving the cookie preferences of a sample of 1,214 adults. If 9% answered "sugar/shortbread," find the decimal and reduced fraction of that percentage.
______decimal
______reduced fraction


Solve for the base. Round to hundredths when necessary.
140 is 120% of what number?


Solve the word problem for the portion, rate, or base.
A quality control process finds 46.8 defects for every 7,800 units of production. What percent of the production is defective?

______%

Answer 1

Answer:

109.26: decimal

5469/50: reduced fraction

140 is 120% of what number?  116.67

What percent of the production is defective?  0.6%

Step-by-step explanation:

For the first one, we know that 1214 is 100%, so we apply the rule of three to find 9% of the sample:

$1214 \rightarrow 100\%\\x\rightarrow 9\%\\\\x=\frac{9*1214}{100}\\\\x=109.26$

Now, to find the reduced fraction we operate with the decimal and then we reduce the resulting fraction:

$109.26*\frac{100}{100} =\frac{10926}{100}\\\\\frac{10926}{100} =\frac{5469}{50}$

For the second exercise we proceed, again, with the rule of three:

$140 \rightarrow 120\%\\x\rightarrow 100\%\\\\x=\frac{100*140}{120}\\\\x=116.67$

For the third question, we will apply the rule of three again:

$7800 \rightarrow 100\%\\46.8\rightarrow x\\\\x=\frac{46.8*100}{7800}\\\\x=0.6\%$