F f f 1 – Casio fx-570MS User Manual
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Explanation
Explanation
Solving Simultaneous Equations
Example 2
Example 2
170 beans are divided among three individuals named A,
B, and C. The ratio of beans given to A and B is 3:5, while
the number of beans given to C is 22 less than the combined total given to
A and B. How many beans each were given to A, B, and C?
Let us say A received
x
number of beans, B
received
y
number of beans, and C received
z
number of beans. This means the total number of beans is
x
+
y
+
z
= 170. Also, since we know the ratio of beans received
between A (
x
) and B (y) is 3:5, we can say 5
x
= 3
y
, which can
be transformed to 5
x
– 3
y
= 0. Finally, since C (
z
) received 22
beans less than A and B combined, we can say
z
=
x
+
y
– 22.
Combining all of this leaves us with the set of simultaneous equations
x
+
y
+
z
= 170
5
x
– 3
y
=
0
x
+
y
–
z
= 22
{
}
, which
we should be able to solve and come up with the answer we need.
*The following shows operation using the fx-100MS/115MS/570MS/991MS.
1
.
Select the EQN Mode and then specify the number of unknowns.
In this example we have three unknowns,
x
,
y
, and
z
so we would specify 3.
F F F 1
(Unknowns?)
3
2
.
Input the values for the coefficients of the linear equations with three unknowns
a
1
x
+
b
1
y
+
c
1
z
=
d
1
a
2
x
+
b
2
y
+
c
2
z
=
d
2
a
3
x
+
b
3
y
+
c
3
z
=
d
3
{
}
.
(a1?)
1
=
(b1?)
1
=
(c1?)
1
=
(d1?)
170
=
(a2?)
5
=
(b2?)
D
3
=
(c2?)
0
=
(d2?)
0
=
(a3?)
1
=
Operation
170
A
B
C