Your mother gave you $9 to buy a gift, which only covered 3/10 of the total cost. how much was the gift?

Step-by-step explanation:

It is useful to label the diagram so we can talk about the parts. (See the attachment.)

AB and CD are parallel lines, crossed by transversal AE. So, angles FAE and CDE are congruent. These are acute angles in a right triangle, so the triangles AFD and DEC are similar by the AA postulate.

This similarity means that corresponding sides are proportional:

  CE/CD = DF/DA

  CE = CD(DF/DA) = 16(6/10) = h

  h = 9.6

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The second problem is identical to the first, but with different numbers.

  CE = CD(DF/DA) = 14(8/10) = h

  h = 11.2