Respuesta :
Explanation
In this kind of exercise, the first step is to define variables (the things you want to find) tagging them by a letter:
x := # of nickels in the purse,
y := # of quarters in the purse.
The next step is to translate the relationship between the variables into equations. In this case, the expression: "There are 15 coins" means
[tex]x+y=15.[/tex]Besides, the expression: "... contains $1.55 in nickels and quarters" means
[tex]0.05x+0.25y=1.55.[/tex]In summary, we have a 2x2 system of linear equations (don't worry about the name):
[tex]\begin{cases}x+y=15 \\ 0.05x+0.25y=1.55\end{cases}[/tex]To solve it, we need to get rid of one variable. Let's eliminate y. Multiplying the second equation by -4, we get
[tex]\begin{gathered} -4\cdot(0.05x+0.25y=1.55), \\ -4\cdot(0.05x)-4\cdot(0.25y)=-4\cdot1.55, \\ -0.2x-y=-6.2. \end{gathered}[/tex]Adding the equation we just obtained with the first in the system, we get
[tex]\begin{gathered} (x+y)+(-0.2x-y)=15-6.2, \\ x-0.2x=8.8, \\ 0.8x=8.8, \\ x=\frac{8.8}{0.8}, \\ x=11. \end{gathered}[/tex]AnswerThe number of nickels in the purse is 11.
The single equation we need to solve the problem is
[tex]0.05x+0.25\cdot(15-x)=1.55.[/tex]