Hints and solutions to
Make a List #4
Jamie and Lynn each worked a different number of days, but each
earned the same amount of money. Use the following clues to find how
many days each worked:
- Jamie earned $15 a day.
- Lynn earned $10 a day.
- Lynn worked 5 more days than Jamie.
-
We have several approaches to this problem.
- In the first, we'll make a systematic
list, using the conditions that Jamie
earns
$15 a day, Lynn earns $10 a day and Lynn works 5 more days than Jamie -
and we'll
see for what number of days the two earn the same amount of money:
Jamie daysJamie earnings
Lynn
daysLynn earnings
1$156$60
2$307$70
3$458$80
4$609$90
5$7510$100
6$9011$110
7$10512$120
8$12013$130
9$13514$140
10$15015$150
So the two will earn the same money if Jamie works 10 days and Lynn works
15.
- We can also approach this problem just by thinking - since
Jamie earns
$5 more per day than Lynn, and Lynn works 5 days more than Jamie, they'll
earn the same if Lynn works the number of days that Jamie earns dollars
per
day and vice versa.
- A third approach would be algebraic - if Jamie works x days, then
Lynn
works x+5 days. Jamie then earns 15x dollars and Lynn earns 10(x+5)
dollars.
Setting these equal and solving does the trick.
Jamie and Lynn each worked a different number of days, but each
earned the same amount of money. Use the following clues to find how
many days each worked:
- Jamie earned $15 a day.
- Lynn earned $10 a day.
- Lynn worked 5 more days than Jamie.
- We have several approaches to this problem.
- In the first, we'll make a systematic
list, using the conditions that Jamie
earns
$15 a day, Lynn earns $10 a day and Lynn works 5 more days than Jamie -
and we'll
see for what number of days the two earn the same amount of money:
Jamie days
Jamie earnings
Lynn days
Lynn earnings
1
$15
6
$60
2
$30
7
$70
3
$45
8
$80
4
$60
9
$90
5
$75
10
$100
6
$90
11
$110
7
$105
12
$120
8
$120
13
$130
9
$135
14
$140
10
$150
15
$150
So the two will earn the same money if Jamie works 10 days and Lynn works 15.
- We can also approach this problem just by thinking - since Jamie earns $5 more per day than Lynn, and Lynn works 5 days more than Jamie, they'll earn the same if Lynn works the number of days that Jamie earns dollars per day and vice versa.
- A third approach would be algebraic - if Jamie works x days, then Lynn works x+5 days. Jamie then earns 15x dollars and Lynn earns 10(x+5) dollars. Setting these equal and solving does the trick.