Per cent Wor d Pr oblems Ratio and proportion method Her e ar e sever al aids t hat will help you solve wor d pr oblems: 1. Make sur e you under st and t he quest ion t hat is asked 2. Sor t out t he inf or mat ion t o make a basic per cent pr oblem, such as 30% of what is 17? 3. Somet imes, you will have t o subt r act or add some of t he number s. 4. The base will always be t he or iginal number, pr ice, or t ot al. Some examples of per cent wor d pr oblems. A baseball pit cher won 80% of t he games he pit ched. I f he pit ched 35 ballgames, how many games did he win? 80% of 35 is what? 80 35 1. Mult iply t he opposit es 80 x 35 = 2800 2. Divide by t he r emaining number 28 2800 28 games J er r y, an elect r ician, wor ked 7 mont hs out of t he year. What per cent of t he year did he wor k? (r ound answer t o t he near est hundr edt h) What per cent of 12 is 7? 12 mont hs = 1 year 7 12 1. Mult iply t he opposit es 7 x = 700 2. Divide by t he r emaining number 58.33 12 700.00 58.33% (r ounded t o hundr edt h) Revised @2009 MLC page 1 of 8
Somet imes t he inf or mat ion needed t o solve a per cent wor d pr oblem is not st at ed dir ect ly. You will need t o sor t out t he number s given in t he pr oblem. Or ganizing all t he inf or mat ion int o a box f or mat will help you see what number s you have and what you need. Some examples. Ther e ar e 28 st udent s in a class. Sixt een of t hose st udent s ar e men. What per cent of t he class ar e women? (Round t o t he near est t ent h) Men % 16 Women % 12 Tot al % 28 28 t ot al st udent s -16 men 12 women 12 is what % of 28? 12 28 1. Mult iple t he opposit es x 12 = 1200 2. Divide by t he r emaining number 42.85 28 1200.00 42.9% ` Donovan t ook a mat h t est and got 35 cor r ect and 10 incor r ect answer s. What was t he per cent age of cor r ect answer s? (Round t o t he near est hundr edt h) Cor r ect answer s % 35 I ncor r ect answer s % 10 Tot al answer s % 45 35 cor r ect answer s +10 incor r ect answer s 45 t ot al answer s 35 is what % of 45? 35 45 1. Mult iple t he opposit es x 35 = 3500 2. Divide by t he r emaining number 77.777 45 3500.000 77.78% (r ounded t o hundr edt h) Revised @2009 MLC page 2 of 8
Per cent Wor d Pr oblems Dir ect ions: Set up a basic per cent pr oblem. Somet imes you will have t o do ext r a st eps t o solve t he pr oblem. Follow r ounding dir ect ions. Answer s and solut ions st ar t on page 6. 1) A st udent ear ned a gr ade of 80% on a mat h t est t hat had 20 pr oblems. How many pr oblems on t his t est did t he st udent answer cor r ect ly? (r ound t o t he near est whole number ) 2) Ther e ar e 36 car pent er s in a cr ew. On a cer t ain day, 29 wer e pr esent. What per cent showed up f or wor k? (r ound t o t he near est t ent h) 3) A met al bar weighs 8.15 ounces. 93% of t he bar is silver. How many ounces of silver ar e in t he bar? (r ound t o t he near est t housandt h) 4) A woman put $ 580 int o a savings account f or one year. The r at e of int er est on t he account was 6½%. How much was t he int er est f or t he year in dollar s and cent s? (Round t o t he near est cent ) Revised @2009 MLC page 3 of 8
5) A st udent answer ed 86 pr oblems on a t est cor r ect ly and r eceived a gr ade 98%. How many pr oblems wer e on t he t est, if all t he pr oblems wer e wor t h t he same number of point s? (Round t o t he near est whole number ) 6) Manuel f ound a wr ecked Tr ans-am t hat he could f ix. He bought t he car f or 65% of t he or iginal pr ice of $ 7200. What did he pay f or t he car? (Round t o near est dollar ) 7) Pamela bought an elect r ic dr ill at 85% of t he r egular pr ice. She paid $ 32.89 f or t he dr ill. What was t he r egular pr ice? (Round t o t he near est cent ) 8) A cr ew is made up of 8 men; t he r est ar e women. 66 3 2 % of t he cr ew ar e men. How many people ar e in t he cr ew? 9) Ben ear ns $ 12,800 a year. About 15% is t aken out f or t axes. How much is t aken out f or t axes? Revised @2009 MLC page 4 of 8
10) At a sale, shir t s wer e sold f or $ 15 each. This pr ice was 80% of t heir or iginal pr ice. What was t he or iginal pr ice? 11) Ther e ar e 32 st udent s in a class. Nine of t hose st udent s ar e women. What per cent ar e men? (r ound t o t he near est t ent h) 12) The Royals sof t ball t eam played 75 games and won 55 of t hem. What per cent of t he games did t hey lose? (r ound t o t he near est t ent h) Revised @2009 MLC page 5 of 8
Answer Key 1. 80 20 80 x 20 = 1600 16 1600 16 pr oblems 2. 29 36 29 x = 2900 80.55 36 2900.00 80.6% 3. 4. 5. 93 8.15 93 x 8.15 = 757.95 7.5795 757.9500 7.580 ounces 6 1 2 580 6 ½ x 580 = 3770 37.70 3770.00 $ 37.70 98 86 x 86 = 8600 87.7 98 8600.0 88 pr oblems (r ounded t o near est whole) Revised @2009 MLC page 6 of 8
6. 7. 8. 65 7200 65 x 7200 = 468,000 4680 468000 $ 4680 85 32.89 x 32.89 = 3289 38.694 85 3289.000 $ 38.69 66 2 3 8 x 8 = 800 800 12 66 2 3 800 1 200 3 4 800 1 3 200 1 12 1 9. 15 12,800 15 x 12,800 = 192,000 1920 192000 $ 1920 10. 80 15 x 15 = 1500 18.75 80 1500.00 Revised @2009 MLC page 7 of 8
11. Tot al % 32 Men 23 Women 9 $ 18.75 32 9 23 23 32 x 23 = 2300 71.87 32 2300.00 71.9%(r ounded t o near est t ent h) 12. Tot al % 75 Won 55 Lost 20 75 55 20 20 75 x 20 = 2000 26.667 75 2000.000 26.7% games lost (r ounded t o t ent h) Revised @2009 MLC page 8 of 8