Answer with explanation:
1. Let x = Number of nickels
y= Number of quarters
Equation: [tex]x+y= 20[/tex] (i)
Equation: [tex]0.05x+0.25y=3[/tex] (ii) [∵ 1 nickel = $0.05 , 1 quarter = $0.25]
Multiply equation (ii) by 20, we get
[tex]x+5y=60[/tex] (iii)
Eliminate (i) from (iii), we get
[tex]4y=40\Rightarrow\ y=10[/tex]
put y= 10 in (i) ,
[tex]x+10=20\Rightarrow\ x=10[/tex]
Sentence = " Jane has 10 nickels and 10 quarters".
2. Let x = Number of dimes
y= Number of nickels
Equation: [tex]x+y= 12[/tex] (i)
Equation: [tex]10x+5y=75[/tex] (ii) [∵ 1 nickel = 5 cents, 1 quarter = 25 cents]
Multiply equation (i) by 5, we get
[tex]5x+5y=60[/tex] (iii)
Eliminate (iii) from (ii), we get
[tex]5x=15\Rightarrow\x=3[/tex]
put x=3 in (i) ,
[tex]3+y=12\Rightarrow\ y=9[/tex]
Sentence = " Joey has 3 dimes and 9 nickels".
