Transcript 13_02 - Using Systems - Age Problems

Solve the following word problem.
The difference of two numbers is nine.
The sum of twice a number and three times
another number is eight.
Find the numbers.
Let:
x = 1st number
x – y = 9
2x + 3y = 8
y = 2nd number
Solve the system
x – y = 9
2x – 2y = 18
–
2x – 3y = – 8
________________
x + 2 = 9
x = 7
– 5y = 10
y = –2
The numbers are 7 and – 2
13.02
Using Systems
to solve
Word Problems
(Age)
A system of equations can be used
to solve various word problems.
To solve a word problem using a system:
1) read the problem carefully
2) set up a system using the information
from the problem,
the variables represent the unknowns
3) solve the system
4) answer the question and
check to see if the answer makes sense
Solve the following word problem.
Alicia is twice as old as Jesus. The sum of the their
ages is 45. How old is Alicia and Jesus?
Let:
a = Alicia’s age
a = 2j
a + j = 45
( 2j ) + j = 45
3j = 45
j = 15
j = Jesus’ age
Solve the system
a = 2j
a = 2(15)
a = 30
Alicia is 30 and Jesus is 15
Solve the following word problem.
Angel is older than Leticia. The sum of their
ages is 30 and the difference of their ages is 2.
How old are Angel and Leticia?
Let:
a = Angel’s age
a + t = 30
a – t = 2
____________
2a = 32
a = 16
t = Leticia’ s age
Solve the system
a + t = 30
16 + t = 30
t = 14
Angel is 16 and Leticia is 14
Solve the following word problem.
The sum of Juan age and his mother’s age is
44.
The sum of Juan’s age and twice his mother’s
age is 76. How old is Juan and his mother.
Let: j = Juan’s age
m = mother’s age
j + m = 44
j + 2m = 76
Solve the system
j + m = 44
j + m = 44
–
j – 2m = – 76
________________
j + 32 = 44
j = 12
– 1m = – 32
m = 32
Juan is 12 and his mother is 32
Solve the following word problem.
Three times Jose’s age minus twice Maria’s age is 22.
Twice Jose’s age plus Maria’s age is 52.
How old are Jose and Maria?
Let:
j = Jose’s age
3j – 2m = 22
2j + m = 52
m = Maria’s age
Solve the system
2j + m = 52
6j – 4m = 44
–
6j – 3m = – 156
__________________
2j + 16 = 52
– 7m = – 112
m = 16
Jose is 18 and Maria is 16
2j = 36
j = 18