Om eenvoudige probleme op te los deur vergelykings te vorm
Aktiwiteit 1
Om eenvoudige probleme te doen deur vergelykings te vorm en op te los
[lu 2.2, 2.4]
Hoe word hierdie probleem gedoen?
Jamie se pa is vier keer so oud as Jamie. Sy pa is 40; hoe oud is Jamie?
a) Miskien moet ons baie hard dink en ‘n paar raaiskote waag, soos: As Jamie 1 is, is sy pa 4. Nie reg nie. Wat van 2 jaar oud? Ensovoorts.
b) Maak ‘n tabel en voltooi die spasies. Help dit?
Ouderdom
1
2
3
4
Ouderdom х 4
4
8
12
28
40
c) Teken ‘n vloeidiagram. Help dit?
Daar is duidelik nie veel verskil tussen die drie metodes nie – jy kan enigeen gebruik wat jou pas. Hulle is egter nie van veel waarde nie, want jy moet nog so baie raai. Vir moeiliker probleme word hierdie metodes onmoontlik om te gebruik.
Gelukkig is daar ‘n beter manier.
Die beste metode om hierdie probleem aan te pak is om ‘n vergelyking vanuit die inligting te vorm. Dan los ons die vergelyking op en skryf die antwoord neer uit die oplossing van die vergelyking.
Dis moeilik om vergelykings te vorm, maar dit word makliker met oefening.
Vir ‘n vergelyking benodig ons ‘n gelykaanteken en ‘n veranderlike (ons gebruik dikwels
x , maar dit kan enige letter wees).
Jamie se pa is vier keer so oud as Jamie. Sy pa is 40; hoe oud is Jamie?
In die algemeen lyk die vergelyking so:
Vier maal Jamie se ouderdom = vader se ouderdom wat 40 is.
Die vraag vereis Jamie se ouderdom; dus:
Laat Jamie se ouderdomxwees .
Nou word die vergelyking: 4
x = 40
Ons moet ‘n getal vind wat 40 gee as ons dit met 4 vermenigvuldig. As ons 40 deur 4 deel, is die antwoord 10. Dus moet
х 10 wees, en Jamie is dus 10 jaar oud. Dis maklik om te bevestig dat dit die korrekte antwoord is.
‘n Probleem vir jou:
Leon het 48 albasters. Amy het slegs ‘n derde soveel as Leon; hoeveel het sy? Gebruik die vorige metode.
Sit jou antwoord op hierdie manier uiteen:
Wat stel die veranderlike voor?.
Skryf ‘n vergelyking met hierdie veranderlike.
Los die vergelyking op.
Skryf die oplossing neer, m.a.w. wat die waarde van die veranderlike is.
Skryf die antwoord op die probleem in woorde neer.
Let op dat die eerste stap en laaste stap in woorde is, en die middelste stappe, algebra.
Oefening:
Vind die antwoorde op die volgende probleme:
1. Mnr. Jacobs het R295,45 in sy sak. Mev. Jacobs het R55,30 minder as haar man in haar handsak. Wat is die bedrag in haar handsak?
2. Ek dink aan ‘n getal. Ek vermenigvuldig dit met 7 en deel die antwoord deur 3. Die resultaat is 49. Wat is die getal waaraan ek gedink het? Onthou om jou antwoord te kontroleer.
3. In Amerika koop Joanie ‘n item wat $5,75 kos. Sy bereken dat dit R41,69 is as sy dollars na rande omskakel. Wat is die dollar–rand wisselkoers wat sy gebruik het?
Aktiwiteit 2
Om doeltreffende metodes te ontwikkel vir moeiliker probleme
[lu 2.3, 2.4]
Ons gaan nog woordsomme doen, maar ons gaan eers op die algebra in die oplossing konsentreer. Maak telkens seker dat jy weet wat elke stap beteken, en waarom dit gedoen word.
Party van die volgende probleme word deur hul oplossings gevolg. Probeer eers om self by die antwoord uit te kom voor jy verder lees. Vergelyk dan jou antwoord en die manier waarop jy dit uiteensit.
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