Answer:
1. t = 48.654
2. [tex]x = \frac{8}{3}[/tex]
3. [tex]s = \frac{49}{4}[/tex]
4. [tex]y = \frac{19}{12}[/tex]
Step-by-step explanation:
To solve equations using variables, perform inverse operations to undo each part and isolate the variable.
1. [tex]\frac{t}{5.4} =9.01[/tex]
Multiply by 5.4 on both sides to undo division.
t = 9.01 * 5.4
t = 48.654
2. [tex]\frac{3}{4}x = 2[/tex]
Multiply both sides by the reciprocal of 3/4 which is 4/3.
[tex]x = 2*\frac{4}{3} \\x = \frac{8}{3}[/tex]
3. [tex]s + \frac{1}{4} = 12\frac{1}{2}[/tex]
Convert 12 1/2 into an improper fraction.
[tex]s + \frac{1}{4} = \frac{25}{2}[/tex]
Subtract 1/4 from both sides.
[tex]s + \frac{1}{4} - \frac{1}{4} = \frac{25}{2} - \frac{1}{4}[/tex]
To subtract fractions without common denominators, convert 25/2 into a fraction with denominator of 4.
[tex]s = \frac{50}{4} - \frac{1}{4}\\s = \frac{49}{4}[/tex]
4. [tex]2\frac{2}{3} + y = 4 \frac{1}{4}[/tex]
Subtract 2 2/3 from both sides.
[tex]2\frac{2}{3} - 2\frac{2}{3} + y = 4 \frac{1}{4}- 2\frac{2}{3}[/tex]
Convert each fraction into improper fractions and then to common denominators.
[tex]y = \frac{17}{4} - \frac{8}{3}\\\\ y = \frac{51}{12} - \frac{32}{12} \\\\y = \frac{19}{12}[/tex]
