Answer:
a. [tex]q + n = 8[/tex]
b. [tex]0.25q + 0.05n = 1.40[/tex]
c. Sarah has 3 nickels and 5 quarters
Sep-by-step explanation:
Given
Coins = 8
Worth = $1.40
Solving (a): Equation relating to number of coins
From the question, we understand that
q = quarters
n = nickels
The required equation is:
[tex]q + n = 8[/tex]
Solving (b): Equation relating to worth of coins
[tex]1\ quarter = \$0.25[/tex]
[tex]1\ nickel = \$0.05[/tex]
So, the equation is
[tex]0.25q + 0.05n = 1.40[/tex]
Solving (c): Values of q and n
Make n the subject of formula in (a)
[tex]n = 8 - q[/tex]
Substitute 8 - q for n in (b)
[tex]0.25q + 0.05(8 - q) = 1.40[/tex]
[tex]0.25q + 0.4 - 0.05q = 1.4[/tex]
Collect Like Terms
[tex]0.25q - 0.05q = 1.4 - 0.4[/tex]
[tex]0.20q = 1.0[/tex]
Make q the subject of formula
[tex]q = \frac{1.0}{0.20}[/tex]
[tex]q = 5[/tex]
Substitute 5 for q in [tex]n = 8 - q[/tex]
[tex]n = 8 - 5[/tex]
[tex]n = 3[/tex]
Hence;
Sarah has 3 nickels and 5 quarters
