Concept explainers
(a)
Write an equation to represent V’s savings y after x weeks.
(a)
Answer to Problem 42PPS
y = 15x + 50
Explanation of Solution
Given:
V is saving his money to buy a new satellite radio for his car.He wants to save enough money for the radio and one year of satellite radio service before he buys it .He started saving for the radio with $50 that he got for his birthday.Since then , he has been adding $15 each week after he cashes his paycheck.
Calculation :
The savings of V = y
Number of weeks = x
Since he saves $15 each week , so , he saves in x weeks = 15x
Initially , he saved $50
So, the total savings after x weeks = 15x + 50
The equation that represents V’s savings y after x weeks :
y = 15x + 50
(b)
Graph the equation is part (a)
(b)
Explanation of Solution
Calculation :
From part (a)
The equation that represents V’s savings y after x weeks :
y = 15x + 50
Make a table to locate the coordinates of the equation:
x | y = 15x + 50 |
0 | 50 |
10 | 200 |
Now, plot the points and join them to draw the graph of the equation y = 15x + 50:
(c)
Find the number of weeks taken by V to save $150.
(c)
Answer to Problem 42PPS
After 7 weeks , V will have atleast $150.
Explanation of Solution
Calculation :
From part (a),
The equation that represents V’s savings y after x weeks :
y = 15x + 50
where
The savings of V = y = $150 (given)
Number of weeks = x
Substitute the value of y in the equation and solve for x :
So, after 7 weeks , V will have atleast $150.
(d)
Find the number of weeks taken by V to save enough money.
(d)
Answer to Problem 42PPS
It will take about 12 weeks to save enough money.
Explanation of Solution
Given:
A satellite radio costs $180 .Satellite radio service costs $10 per month.V started saving two weeks ago.
Calculation :
From part (a),
The equation that represents V’s savings y after x weeks :
y = 15x + 50
where
The savings of V = y = $150 (given)
Number of weeks = x
He wants to pay for the radio and 1 year of service, so , total amount required by V is :
He is saving for two weeks now , so, the amount V has already saved :
So, he has $80 with him already.
Now, he needs to save = $300 - $80 = $220
So, substitute y = 220 in the equation to find the number of weeks:
So, it will take about 12 weeks to save enough money.
Chapter 3 Solutions
Geometry, Student Edition
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