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1. The system of linear equation which can be used to find the number of nickles n, and quarters q Anatoily has are n + q = 104  and 1/20(104 – q) + (1/4)q = 22there are total 20 nickels and 84 quarters Anatoily has.

   According to the given question.

   Total number of nickles and quarters Anatoily have is 104.

   ‘n’ represents the total numbers of nickles and ‘q’ represents total number of quarters. So, the linear equation which represents the given condition

   ⇒ n + q = 104

   Since, 20nickles = 1 dollar

   ⇒ 1 nickle = 1/20 dollar

   And, 4 quarters = 1 dollar

   ⇒ 1quarter = 1/4 dollar

   Here, it is also given that combination of 104 nickels and quarters totaling $22.

   So, we have an other linear equation $(1/20)n + $(1/4)q = $22

   Form

   n + q = 104

   We can write

   n = 104 – q

   Substitute the value of n in $(1/20)n + $(1/4)q = $22

   Therefore,

   $1/20(104 – q) + $(1/4)q = $22

   ⇒ 5.2 – q/20 + q/4 = 22

   ⇒ 5.2 +  (-q + 5q)/20 = 22

   ⇒ 5.2 + 4q/20 = 22

   ⇒ 5.2 + q/5 = 22

   ⇒ q/5 = 22 – 5.2

   ⇒ q/5 = 16.8

   ⇒ q = 16.8 × 5

   ⇒ q = 84

   Therefore,

   n = 104 – 84

   ⇒ n = 20

   Hence,  the system of linear equation which can be used to find the number of nickles n, and quarters q Anatoily has are n + q = 104  and 1/20(104 – q) + (1/4)q = 22there are total 20 nickels and 84 quarters Anatoily has.

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