1. A private organization distributed 5-kilo rice packs to a certain barangay placed under special lockdown due to COVID 19. If the rice sells at P40 per kilogram, how much did the organization spent if a total of 125 rice packs of rice was given?
Given:
1 pack = 5 kg rice
1 kg of rice = P 40
125 rice packs were given
Amount spent = ?
Solution:
First, let’s compute the amount of money spent for one rice pack. Note that 1 pack = 5 kg of rice, and 1 kg. of rice = Php 40.00.
[tex]1\ pack = (5\ \cancel{kg.\ of\ rice}) \times \frac{Php\ 40.00}{1\ \cancel{kg.\ of\ rice}} = Php\ 200.00[/tex]
Therefore, one pack costs Php 200.00.
If there are 125 rice packs given and 1 pack = Php 200.00, then…
[tex]125\ rice\ packs \times Php\ 200.00 = \Large{\boxed{Php\ 25,000}}[/tex]
Let f(x) be the total amount spent.
[tex]f(x) = 125\ \cancel{rice\ packs} \times \frac{5\ \cancel{kg.\ of\ rice}}{1\ \cancel{rice\ pack}} \times \frac{Php\ 40.00}{1\ \cancel{kg.\ of\ rice}} = \boxed{Php\ 25,000}[/tex]
Answer:
[tex]\tt{The\ government\ spent\ Php\ 25,000\ to\ distribute\ 125\ rice\ packs.}[/tex]
2. An express delivery driver earns P500 daily for an eight-hour shift and an additional P35 for every hour after that. Generate a function to solve his total earnings.
Given:
8 hours = Php 500.00
[tex]< 8\ hours = Php\ 500 + (Php\ 35 \times number\ of\ additional\ hours)[/tex]
Mathematical function:
Let x be the number of hours after the eight-hour shift.
[tex]\Large{\boxed{f(x) = 500 + 35x}}[/tex]
3. A computer shop charges P15 for the first hour and P10 for the succeeding hours. If Jacob pays P45, how many hours did he rent the computer?
Given:
First hour = Php 15
[tex]< 1\ hour = Php\ 15 + (Php\ 10 \times number\ of\ succeeding\ hours)[/tex]
Total payment = Php 45
Mathematical function:
Let x be the number of succeeding hours.
[tex]\boxed{f(x) = 15 + 10x}[/tex]
Solution:
Let f(x) be the total payment.
[tex]45 = 15 + 10x\\45 – 15 = 10x\\30 = 10x\\x = \frac{30}{10}\\x = 3[/tex]
Answer:
[tex]\tt{Jacob\ rent\ the\ computer\ for\ 3\ hours.}[/tex]
4. Ichan bought a car, he puts Php 25 000 down payment and make monthly payment of Php12 000. If his car cost Php 457 000, how many years will it take him to pay it off?
Given:
Down payment = Php 25,000
Monthly payment = Php 12,000
Total payment = Php 457,000
Years to pay = ?
Mathematical function:
[tex]Months\ to\ pay = \frac{Total\ payment\ - Down\ payment}{Monthly\ payment}\\ Months\ to\ pay = \frac{Php\ 457,000\ - Php\ 25,000}{Php\ 12,000}[/tex]
Solution:
[tex]Months\ to\ pay = \frac{Php\ 457,000\ - Php\ 25,000}{Php\ 12,000}\\= \frac{Php\ 432,000}{Php\ 12,000}\\= 36[/tex]
Change 36 months to years. Note: 1 year = 12 months
[tex]\frac{36\ \cancel{months}}{1} \times \frac{1\ year}{12\ \cancel{months}} = \Large{\boxed{3\ years}}[/tex]
Answer:
[tex]\tt{Ichan\ will\ take\ 3\ years\ to\ pay\ the\ car.}[/tex]
5. Riza earns Php 90 an hour in a toy factory with an additional of Php 45 for her daily meal allowance. On a Tuesday, she earned a total of Php 585, how many hours did she work for that day?
Given:
1 hour = Php 90.00
Daily meal (additional) = Php 45.00
Total earned (Tuesday) = Php 585.00
Hours worked = ?
Mathematical function:
Let f(x) be the total earned on Tuesday and x be the number of hours Riza worked.
[tex]f(x) = 90x + 45[/tex]
[tex]585 = 90x + 45\\585 - 45 = 90x\\540 = 90x\\x = \frac{540}{90}\\x = 6[/tex]
Answer:
[tex]\tt{Riza\ worked\ for\ 6\ hours\ on\ Tuesday.}[/tex]
[tex]\pink{\overbrace{\underbrace{\rm{Happy\ learning!}}}}[/tex]
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