# 9.6.1. Solving Two First-Degree Equations Algebraically and Geometrically

If a sum of LE is to be changed into 44 banknotes which have the values of piastres and piastres, find the number of the banknotes needed from each type.

• A36 of piastres, 8 of piastres
• B156 of piastres, 136 of piastres
• C8 of piastres, 36 of piastres
• D136 of piastres, 156 of piastres

### Example

If a sum of LE is to be changed into 44 banknotes which have the values of piastres and piastres, find the number of the banknotes needed from each type.

### Solution

Let the number of banknotes with a value of 25 piastres be denoted by and the number of banknotes with a value of 50 piastres be denoted by . Then the equation for the number of each note is

Since is equivalent to , therefore the equation for the value of the notes is

Dividing by 25 gives

This pair of equations can be solved using the omitting method. Subtracting the two equations gives

Substituting this value of into the first equation gives

Therefore, there are 8 notes of 25 piastres and 36 notes of 50 piastres.

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