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2023 UMD Math Competition Part I
#18
Ordered triples
Ordered triples
Source: UMD 2023 I #18
October 22, 2023
UMD
algebra
Problem Statement
How many ordered triples of integers
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
satisfy the following system?
{
a
b
+
c
=
17
a
+
b
c
=
19
\begin{cases} ab + c &= 17 \\ a + bc &= 19 \end{cases}
{
ab
+
c
a
+
b
c
=
17
=
19
a
.
2
b
.
3
c
.
4
d
.
5
e
.
6
\mathrm a. ~ 2\qquad \mathrm b.~3\qquad \mathrm c. ~4 \qquad \mathrm d. ~5 \qquad \mathrm e. ~6
a
.
2
b
.
3
c
.
4
d
.
5
e
.
6
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