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Proportions and Equations

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Proportions and Equations
Remember that RATES in these equations must be expressed as decimals.
Examples: 8% = .08 7.5% = .075
20% = .20 or .2
5.25% = .0525
OPTION A
12.5% = .125
π‘ π‘’π‘π‘‘π‘œπ‘‘π‘Žπ‘™ π‘₯ π‘ π‘Žπ‘™π‘’π‘  π‘‘π‘Žπ‘₯ π‘Ÿπ‘Žπ‘‘π‘’ = π‘ π‘Žπ‘™π‘’π‘  π‘‘π‘Žπ‘₯
π‘ π‘’π‘π‘‘π‘œπ‘‘π‘Žπ‘™ + π‘ π‘Žπ‘™π‘’π‘  π‘‘π‘Žπ‘₯ = π‘‘π‘œπ‘‘π‘Žπ‘™
OPTION B
π‘ π‘’π‘π‘‘π‘œπ‘‘π‘Žπ‘™ π‘₯ (1 + π‘ π‘Žπ‘™π‘’π‘  π‘‘π‘Žπ‘₯ π‘Ÿπ‘Žπ‘‘π‘’) = π‘‘π‘œπ‘‘π‘Žπ‘™
π‘ π‘’π‘π‘‘π‘œπ‘‘π‘Žπ‘™ π‘₯ π‘”π‘Ÿπ‘Žπ‘‘π‘’π‘–π‘‘π‘¦/𝑑𝑖𝑝 π‘Ÿπ‘Žπ‘‘π‘’ = π‘”π‘Ÿπ‘Žπ‘‘π‘’π‘–π‘‘π‘¦/𝑑𝑖𝑝
π‘ π‘’π‘π‘‘π‘œπ‘‘π‘Žπ‘™ + π‘”π‘Ÿπ‘Žπ‘‘π‘’π‘–π‘‘π‘¦/𝑑𝑖𝑝 = π‘‘π‘œπ‘‘π‘Žπ‘™
π‘‘π‘œπ‘‘π‘Žπ‘™ π‘ π‘Žπ‘™π‘’π‘  π‘₯ π‘π‘œπ‘šπ‘šπ‘–π‘ π‘ π‘–π‘œπ‘› π‘Ÿπ‘Žπ‘‘π‘’ = π‘π‘œπ‘šπ‘šπ‘–π‘ π‘ π‘–π‘œπ‘›
π‘π‘Žπ‘ π‘’ π‘π‘Žπ‘¦ + π‘π‘œπ‘šπ‘šπ‘–π‘ π‘ π‘–π‘œπ‘› = π‘‘π‘œπ‘‘π‘Žπ‘™
π‘ π‘’π‘π‘‘π‘œπ‘‘π‘Žπ‘™ π‘₯ 𝑓𝑒𝑒 π‘Ÿπ‘Žπ‘‘π‘’ = 𝑓𝑒𝑒 π‘Žπ‘šπ‘œπ‘’π‘›π‘‘
π‘ π‘’π‘π‘‘π‘œπ‘‘π‘Žπ‘™ + 𝑓𝑒𝑒 π‘Žπ‘šπ‘œπ‘’π‘›π‘‘ = π‘‘π‘œπ‘‘π‘Žπ‘™
π‘œπ‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π‘π‘Ÿπ‘–π‘π‘’ π‘₯ π‘šπ‘Žπ‘Ÿπ‘˜π‘’π‘ π‘Ÿπ‘Žπ‘‘π‘’ = π‘šπ‘Žπ‘Ÿπ‘˜π‘’π‘ π‘Žπ‘šπ‘œπ‘’π‘›π‘‘
OPTION A
π‘œπ‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π‘π‘Ÿπ‘–π‘π‘’ + π‘šπ‘Žπ‘Ÿπ‘˜π‘’π‘ π‘Žπ‘šπ‘œπ‘’π‘›π‘‘ = π‘‘π‘œπ‘‘π‘Žπ‘™
OPTION B
OPTION A
π‘œπ‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π‘π‘Ÿπ‘–π‘π‘’ π‘₯ (1 + π‘šπ‘Žπ‘Ÿπ‘˜π‘’π‘ π‘Ÿπ‘Žπ‘‘π‘’) = π‘‘π‘œπ‘‘π‘Žπ‘™
π‘œπ‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π‘π‘Ÿπ‘–π‘π‘’ π‘₯ π‘šπ‘Žπ‘Ÿπ‘˜π‘‘π‘œπ‘€π‘›/π‘‘π‘–π‘ π‘π‘œπ‘’π‘›π‘‘ π‘Ÿπ‘Žπ‘‘π‘’ = π‘šπ‘Žπ‘Ÿπ‘˜π‘‘π‘œπ‘€π‘›/π‘‘π‘–π‘ π‘π‘œπ‘’π‘›π‘‘ π‘Žπ‘šπ‘œπ‘’π‘›π‘‘
π‘œπ‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π‘π‘Ÿπ‘–π‘π‘’ − π‘šπ‘Žπ‘Ÿπ‘˜π‘‘π‘œπ‘€π‘›π‘‘π‘–π‘ π‘π‘œπ‘’π‘›π‘‘ π‘Žπ‘šπ‘œπ‘’π‘›π‘‘ = π‘šπ‘Žπ‘Ÿπ‘˜π‘‘π‘œπ‘€π‘›/π‘‘π‘–π‘ π‘π‘œπ‘’π‘›π‘‘ π‘π‘Ÿπ‘–π‘π‘’
OPTION B
π‘œπ‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π‘π‘Ÿπ‘–π‘π‘’ π‘₯ (1 − π‘šπ‘Žπ‘Ÿπ‘˜π‘‘π‘œπ‘€π‘›/π‘‘π‘–π‘ π‘π‘œπ‘’π‘›π‘‘ π‘Ÿπ‘Žπ‘‘π‘’) = π‘šπ‘Žπ‘Ÿπ‘‘π‘œπ‘€π‘›/π‘‘π‘–π‘ π‘π‘œπ‘’π‘›π‘‘ π‘π‘Ÿπ‘–π‘π‘’
Remember that RATES in these equations must be expressed as decimals.
Examples: 8% = .08 7.5% = .075
20% = .20 or .2
5.25% = .0525
𝐼 = π‘π‘Ÿπ‘‘
12.5% = .125
I = interest
p = principal (original amount)
r = rate (years)
t = time (in YEARS)
π‘π‘Ÿπ‘–π‘›π‘π‘–π‘π‘Žπ‘™ + π‘–π‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘ = π‘‘π‘œπ‘‘π‘Žπ‘™
If the time is given in the problem in months instead of years, you can simply place the number
of months over 12 in your equation.
πŸ’
Examples: 4 months would be 𝟏𝟐 of a year
πŸ—
9 would be 𝟏𝟐 of a year
𝑁𝑒𝑀 π΄π‘šπ‘œπ‘’π‘›π‘‘−π‘‚π‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π΄π‘šπ‘œπ‘’π‘›π‘‘
π‘‚π‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π΄π‘šπ‘œπ‘’π‘›π‘‘
π‘‚π‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π΄π‘šπ‘œπ‘’π‘›π‘‘−𝑁𝑒𝑀 π΄π‘šπ‘œπ‘’π‘›π‘‘
π‘‚π‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π΄π‘šπ‘œπ‘’π‘›π‘‘
|
πΈπ‘ π‘‘π‘–π‘šπ‘Žπ‘‘π‘’π‘‘ π‘‰π‘Žπ‘™π‘’π‘’ –π΄π‘π‘‘π‘’π‘Žπ‘™ π‘‰π‘Žπ‘™π‘’π‘’
π΄π‘π‘‘π‘’π‘Žπ‘™ π‘‰π‘Žπ‘™π‘’π‘’
π‘₯ 100
π‘₯ 100
| π‘₯ 100
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