Question

Joan and Marcus took two different exams. Joan scored 36 out of a total possible 40 and Marcus scored 42 out of a total possible 70 on his exam. Who earned the higher grade and how much percentage he scored?

• A. $\text{Marcus}$, $60$%
• B. $\text{Joan}$, $90$%
• C. $\text{Marcus}$, $90$%
• D. $\text{Joan}$, $60$%

Answer 1

The correct option is B $\text{Joan}$, $90$%

Step 1: Convert the grades into fractions
Joan$=\frac{36}{40}$
Marcus$=\frac{42}{70}$

Step 2: Convert the fractions into percentages
$\frac{36}{40}=\frac{?}{100}$

Do cross multiplication :

$?\times 40=100\times 36$
$?=\frac{100\times 36}{40}$
$?=\frac{10\times 10\times 9\times 4}{4\times 10}$
$?=90$

$\Rightarrow \frac{36}{40}=\frac{90}{100}$
$=90$%
Joan's grade $=90$%

Now, repeat the above process to get $?$ for the equation $\frac{42}{70}=\frac{?}{100}$

$\frac{42}{70}=\frac{?}{100}$

$?=\frac{100\times 42}{70}$
$?=60$

$\Rightarrow \frac{42}{70}=\frac{60}{100}$

$=60$%
Marcus's grade$=60$%

Step 3: Compare the grades to see who got a higher grade
Joan's grade $=90$%
Marcus's grade $=60$%
So,
Joan's grade is higher than Marcus's grade and he got $90$%.