[tex]1) \frac{x}{y} = \frac{2}{3} [/tex]
[tex]3x = 2y[/tex]
[tex]x = \frac{2y}{3} [/tex]
[tex] \frac{6x + y}{x + 3y} = \frac{6 \times \frac{2y}{3} + y}{ \frac{2y}{3} + 3y } = \frac{ \frac{12y}{3} + y}{ \frac{2y}{3} + \frac{9y}{3} } = \frac{4y + y}{ \frac{2y + 9y}{3} } [/tex]
[tex] = \frac{5y}{ \frac{11y}{3} } = 5y \times \frac{3}{11y} = \frac{5y \times 3}{11y} = \frac{15y}{11y} = \frac{15}{11} [/tex]
[tex]2)A = {l}^{2} [/tex]
[tex]A= 169[/tex]
[tex] {l}^{2} = 169[/tex]
[tex]l = \sqrt{169} [/tex]
[tex]l = 13[/tex]
[tex]A = 196[/tex]
[tex] {l}^{2} = 196[/tex]
[tex]l = \sqrt{196} [/tex]
[tex]l = 14[/tex]
[tex]P = 4l[/tex]
[tex]P = 4 \times 13 = 52[/tex]
[tex]P = 4 \times 14 = 56[/tex]
[tex]3)a) \frac{15}{100} \times 2500 = 15 \times 25 = 375[/tex]
[tex]b) \frac{0.4}{100} \times \frac{120}{17} = \frac{ \frac{4}{10} }{100} \times \frac{120}{17} [/tex]
[tex] = \frac{4}{10} \times \frac{1}{100} \times \frac{120}{17} = \frac{4}{10} \times \frac{1}{10} \times \frac{12}{17} [/tex]
[tex] = \frac{4 \times 1 \times 12}{10 \times 10 \times 17} = \frac{48}{1700} = \frac{24}{850} = \frac{12}{425} [/tex]
[tex]4)b + f = 25[/tex]
[tex]f = \frac{60}{100} \times 25 = \frac{60}{4} = 15[/tex]
[tex]b + 15 = 25[/tex]
[tex]b = 25 - 15[/tex]
[tex]b = 10[/tex]
[tex]\frac{x}{100}\times f=b[/tex]
[tex]\frac{x}{100}\times 15=10[/tex]
[tex]\frac{15x}{100}=10[/tex]
[tex]15x=100\times10[/tex]
[tex]15x=1000[/tex]
[tex]x=\frac{1000}{15}[/tex]
[tex]x=66.(6)[/tex]
[tex]x=66.66[/tex]
[tex]5) \frac{a}{b} = \frac{2}{3} [/tex]
[tex]3a = 2b[/tex]
[tex]a = \frac{2b}{3} [/tex]
[tex]a - b = 15[/tex]
[tex] \frac{2b}{3} - b = 15 \: | \times 3[/tex]
[tex]2b - 3b = 45[/tex]
[tex] - b = 45 \: | \times ( - 1)[/tex]
[tex]b = - 45[/tex]
[tex]a = \frac{2b}{3} = \frac{2 \times ( - 45)}{3} = - \frac{90}{3} = - 30[/tex]
[tex]6) \frac{a}{0.1} = \frac{20}{b} [/tex]
[tex]ab = 0.1 \times 20[/tex]
[tex]ab = 2[/tex]
[tex]17 + ab = 17 + 2 = 19[/tex]
