Answer
a) The system of two linear inequalities include
5x + 3y ≥ 15
3x + 4y > 12
b) Least number of times Sally needs to play only the ring toss in order to achieve her goal of more than 12 tickets = 5
c) Least number of times Tom needs to play only the fishing game in order to achieve her goal of at least 15 tickets = 5
Step-by-step explanation
Number of times Ring toss needs to be played is denoted as x.
Number of times Fishing game needs to be played is denoted as y.
a) For Tom
5 tickets for each ring toss = 5x
3 tickets for each fishing game = 3y
Tom needs at least 15 tickets for the prize he wants
5x + 3y ≥ 15
For Sally
3 tickets for each ring toss = 3x
4 tickets for each fishing game = 4y
Sally needs more than 12 tickets for the prize she wants
3x + 4y > 12
The system of two linear inequalities is then
5x + 3y ≥ 15
3x + 4y > 12
b) What is the least number of times Sally needs to play only the ring toss in order to have enough tickets for the prize she wants?
The inequality describing her situation is
3x + 4y > 12
We are now told that if she plays only the ring toss, (that is, no fishing game, y = 0), what would be the minimum number of times she would need to play to achieve her goal of more than 12 tickets?
3x + 4y > 12
when y = 0
3x + 4y > 12
3x + 4(0) > 12
3x + 0 > 12
3x > 12
Divide both sides by 3
(3x/3) > (12/3)
x > 4
Number of times has to be more than 4, so, minimum number of times has to be 5.
c) What is the least number of times Tom needs to play only the fishing game in order to have enough tickets for the prize he wants?
The inequality describing his situation is
5x + 3y ≥ 15
We are now told that if he plays only the fishing game, (that is, no ring toss, x = 0), what would be the minimum number of times he would need to play to achieve his goal of at least 15 tickets?
5x + 3y ≥ 15
when x = 0
5(0) + 3y ≥ 15
0 + 3y ≥ 15
3y ≥ 15
Divide both sides by 3
(3y/3) ≥ (15/3)
y ≥ 5
Number of times has to be at least 5, so, minimum number of times has to be 5.
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