The complete question is:
Suppose you have just enough money, in coins, to pay for a loaf of bread priced at $1.95. You have 12 coins, all quarters, and dimes. Let q equal the number of quarters and d equal the number of dimes. Which system models the given information?
a.
q + d = 12
q + d = 1.95
b.
0.10q + 0.25d = 12
q + d = 1.95
c.
25q + 10d = 1.95
q + 12 = d
d.
q + d = 12
0.25q + 0.10d = 1.95
Answer:
The system models the given information as option (d) [tex]&q+d=12 \\[/tex]
[tex]&0.25 q+0.10 d=1.95[/tex].
How to estimate the system model of the given information?
Given is, you have q quarters and d dimes totaling 12 coins, all of which are either quarters or dimes,
[tex]$q+d=12 ........... (1)[/tex]
We know that the value of a quarter is 25 cents
So the value of all q quarters is [tex]$25 q$[/tex] cents.
Similarly, the value of your d dimes is [tex]$10 d$[/tex] cents.
Now given the total value of your money is [tex]$\$ 1.95=195$[/tex] cents so the equation is :
[tex]$25 q+10 d=195$[/tex] or the value of the quarters can be given as [tex]$0.25 q$[/tex] and the value of dimes as [tex]$0.10 \mathrm{~d}$[/tex],
making equation
[tex]$0.25 q+0.10 d=1.95 \ldots .(2)$[/tex]
Therefore, the correct answer is option (d).
q + d = 12
0.25q + 0.10d = 1.95
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