Answer:
a. The unknowns in the equation above are q and d that represent the number of quarters and dimes respectively.
b. The two equations that need to be solved are; q+d=60...equation 1, and
0.25 q+0.1 d=9.45...equation 2
c.
Number of dimes, d=37
Number of quarters, q=23
Explanation:
a.
<em>Step 1: Derive equation for determining total number of coins.</em>
The total number of coins can be derived using the expression below;
T=q+d
where;
T=total number of coins
q=number of quarters
d=number of dimes
In our case;
T=60 coins
q=unknown
d=unknown
replacing;
q+d=60...equation 1
The unknowns in the equation above are q and d that represent the number of quarters and dimes respectively.
b.
<em>Step 2: Derive equation for determining combined value of coins.</em>
V=(q×Q)+(d×D)
where;
V=total value of the coins
q=number of quarters
Q=unit value of a quarter in dollars
d=number of dimes
D=unit value of a dime in dollars
In our case;
V=$9.45
q=unknown
Q=$0.25
d=unknown
D=$0.10
replacing;
9.45=(0.25×q)+(0.10×d)
9.45=0.25 q+0.1 d
0.25 q+0.1 d=9.45...equation 2
<em>Step 3: Combine equation 1 and 2 and solve simultaneously</em>
(q+d=60)×0.25 >>>>>>>>>>>> 0.25 q+0.25 d=15
-
(0.25 q+0.1 d=9.45)×1>>>>>>> 0.25 q+0.1 d=9.45
(0.25 q-0.25 q)+(0.25 d-0.1 d)=15-9.45
0 q+0.15 d=5.55
0.15 d=5.55
d=5.55/0.15=37
d=37
Substitute the value of d in equation 1;
q+d=60
and q=37
37+q=60
q=60-37=23
q=23
