Students are given 3 minutes for each multiple-choice question and 5 minutes for each free-response question on a test. there are 15 questions on the test, and students are given 51 minutes to take it.
the system of equations shown can be used to find the number of multiple-choice questions, m, and the number of free-response questions, f, on the test.
m + f = 15
3m + 5f = 51
how many multiple-choice questions are on the test?

There are 12 multiple choice questions.

Step-by-step explanation:

The given equations are :

    .. (1)

  ... (2)

Multiplying (1) by 3 and subtracting from (2)

Equation 1 becomes:

Subtracting this from 2, we get

=>

f=3

And as

Substituting f = 3, we get

So,

Hence, there are 12 multiple choice questions.

13

step-by-step explanation:

169-1=168

168-3=165

165-5=160

160-7=153

153-9=144

144-11=133

133-13=120

120-15=105

105-17=88

88-19=69

69-21=48

48-23=25

25-25=0

since it took 13times to completely subtract it hence its square root is 13

details

step-by-step explanation: