If the average of the first four of five numbers in decreasing order is 25 and the average of the last four numbers is 20, then what is the difference between the first and the last number?<\/p>\n
[amp_mcq option1=”5″ option2=”10″ option3=”15″ option4=”20″ correct=”option4″]<\/p>\n
The average of the first four numbers is 25.
\n$(n_1 + n_2 + n_3 + n_4) \/ 4 = 25$
\nThe sum of the first four numbers is $n_1 + n_2 + n_3 + n_4 = 25 \\times 4 = 100$. (Equation 1)<\/p>\n
The average of the last four numbers is 20.
\n$(n_2 + n_3 + n_4 + n_5) \/ 4 = 20$
\nThe sum of the last four numbers is $n_2 + n_3 + n_4 + n_5 = 20 \\times 4 = 80$. (Equation 2)<\/p>\n
We need to find the difference between the first and the last number, which is $n_1 – n_5$.<\/p>\n
Subtract Equation 2 from Equation 1:
\n$(n_1 + n_2 + n_3 + n_4) – (n_2 + n_3 + n_4 + n_5) = 100 – 80$<\/p>\n
Expanding the left side:
\n$n_1 + n_2 + n_3 + n_4 – n_2 – n_3 – n_4 – n_5 = 100 – 80$<\/p>\n
The terms $n_2, n_3, n_4$ cancel out:
\n$n_1 – n_5 = 20$<\/p>\n