Certainly! Let's work through each question step by step:
Q2. Four-fifths of a number is greater than three-fourths of a number by 8. Find the number.
1. Let's denote the unknown number as [tex]\( x \)[/tex].
2. According to the problem, four-fifths of the number ([tex]\( \frac{4}{5}x \)[/tex]) is greater than three-fourths of the number ([tex]\( \frac{3}{4}x \)[/tex]) by 8. Therefore, we can write the equation:
[tex]\[
\frac{4}{5}x = \frac{3}{4}x + 8
\][/tex]
3. To solve for [tex]\( x \)[/tex], first get all the [tex]\( x \)[/tex]-terms on one side of the equation. Subtract [tex]\( \frac{3}{4}x \)[/tex] from both sides:
[tex]\[
\frac{4}{5}x - \frac{3}{4}x = 8
\][/tex]
4. To subtract these fractions, find a common denominator. The common denominator for 5 and 4 is 20:
[tex]\[
\frac{16}{20}x - \frac{15}{20}x = 8
\][/tex]
5. Simplify the left side of the equation:
[tex]\[
\frac{1}{20}x = 8
\][/tex]
6. Multiply both sides by 20 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 8 \times 20
\][/tex]
[tex]\[
x = 160
\][/tex]
Therefore, the number is 160.
Q3. Ten added to thrice a whole number gives 40. Find the number.
1. Let's denote the unknown number as [tex]\( y \)[/tex].
2. According to the problem, ten added to three times the number ([tex]\( 3y \)[/tex]) equals 40. Therefore, we can write the equation:
[tex]\[
3y + 10 = 40
\][/tex]
3. To solve for [tex]\( y \)[/tex], first subtract 10 from both sides of the equation:
[tex]\[
3y = 40 - 10
\][/tex]
[tex]\[
3y = 30
\][/tex]
4. Divide both sides by 3 to isolate [tex]\( y \)[/tex]:
[tex]\[
y = \frac{30}{3}
\][/tex]
[tex]\[
y = 10
\][/tex]
Therefore, the number is 10.
