Question

Seven times the number is 36 less than 10 times the number. Find the number. e. 4/5 of a number is more than 3/4 of the number by 5. Find the number. f. Among the two supplementary angles, the measure of the larger angle is 36° more than the measure of smaller. Find their measures.

Answer 1

${\large{\underline{\pmb{\sf{RequirEd \; Solution...}}}}}$

${\underline{\boxed{\bf{Question \; 1 : }}}}$

${\bigstar\;{\underline{\purple{\underline{\pmb{\sf{Given\; that...}}}}}}}$

⋆ Seven times the number is 36 less than 10 times the number

${\bigstar\;{\underline{\purple{\underline{\pmb{\sf{To \; Find...}}}}}}}$

⋆ The unknown number which would satisfy the statement.

${\bigstar\;{\underline{\purple{\underline{\pmb{\sf{Understanding \; concept...}}}}}}}$

⋆Now, we have been given a statement that Seven times the number is 36 less than 10 times the number

⋆ So, let's assign a variable to the number as it is undefined and frame an equation according to the statement

${\bigstar\;{\underline{\purple{\underline{\pmb{\sf{Full \; Solution...}}}}}}}$

⋆ Framing an equation we get,

${:\implies}\sf 7x = 10x - 36$

${:\implies}\sf 36 = 10x - 7x$

${:\implies}\sf 36 = 3x$

${:\implies}\sf x = \dfrac{36}{3}$

${:\implies}\sf x = 12$

• Henceforth the required number is 12

${\underline{\boxed{\bf{Question \; 2 : }}}}$

${\bigstar\;{\underline{\purple{\underline{\pmb{\sf{Given\; that...}}}}}}}$

⋆ 4/5 of a number is more than 3/4 of the number by 5

${\bigstar\;{\underline{\purple{\underline{\pmb{\sf{To \; Find...}}}}}}}$

⋆ The unknown number which would satisfy the statement.

${\bigstar\;{\underline{\purple{\underline{\pmb{\sf{Understanding \; concept...}}}}}}}$

⋆ Now, we have been given a statement that, 4/5 of a number is more than 3/4 of the number by 5

⋆ So, let's assign a variable to the number as it is undefined and frame an equation according to the statement.

${\bigstar\;{\underline{\purple{\underline{\pmb{\sf{Full \; Solution...}}}}}}}$

⋆ Framing an equation we get,

${:\implies}\sf \dfrac{4}{5} x = \dfrac{3}{4} x + 5$

${:\implies}\sf \dfrac{4x}{5} = \dfrac{3x}{4} + 5$

${:\implies}\sf \dfrac{4x}{5} - \dfrac{3x}{4} = 5$

${:\implies}\sf \dfrac{16x-15x}{20} =5$

${:\implies}\sf \dfrac{x}{20} = 5$

${:\implies}\sf x = 100$

• Henceforth the number is 100

${\underline{\boxed{\bf{Question \; 3 : }}}}$

${\bigstar\;{\underline{\purple{\underline{\pmb{\sf{Given\; that...}}}}}}}$

⋆ Among the two supplementary angles, the measure of the larger angle is 36° more than the measure of smaller.

${\bigstar\;{\underline{\purple{\underline{\pmb{\sf{To \; Find...}}}}}}}$

⋆ The measures of the two angles.

${\bigstar\;{\underline{\purple{\underline{\pmb{\sf{Understanding \; concept...}}}}}}}$

⋆ here, we have been given that the measure of the larger angle is 36° more than the measure of smaller.

⋆ So, let's assign a variable to the smaller angle as it is undefined and frame an equation according to the statement.

${\bigstar\;{\underline{\purple{\underline{\pmb{\sf{Full \; Solution...}}}}}}}$

⋆ Framing an equation we get,

${:\implies}\sf x + x + 36\degree = 180\degree$

${:\implies}\sf 2x + 36\degree = 180\degree$

${:\implies}\sf 2x = 180\degree - 36\degree$

${:\implies}\sf 2x = 144\degree$

${:\implies}\sf x = \dfrac{144}{2}$

${:\implies}\sf x = 72\degree$

⋆ Now, let's find the angles

$\longrightarrow \tt smaller\; angle = x = 72\degree$

${\longrightarrow}\tt larger\; angle = x + 36\degree = 72\degree + 36\degree = 108\degree$

• Henceforth the measures of the angles are 72, 106 degrees