Jason is counting the number of cars that drive by his window. He counted four times as many green cars as red cars, and 6 more red cars than purple cars. If he counted 312 cars total, how many of them were purple?

How many green cars are there? ** Let g be the number of green cars, r be the number of red cars, and p be the number of purple cars. We know that g + r + p = 315, r = p + 6, and g = 4r

How many green cars are there? ** Substitute the second equation into the third equation to get: g = 4r = 4(p + 6) = 4p + 24

Write an equation ** Now substitute the equations that express g and r in terms of p in the equation for the total number of cars: 4p + 24 + p + 6 + p = 315

Combine like terms ** Now combine like terms to get 6p + 30 = 312

Subtract 30 ** Now subtract 30 from both sides to get 6p = 282

Divide by 6 ** Now divide both sides by 6 to get p = 47

#### 47

Brittany, Alex, and Jamy all share 600 marbles divided between them in the ratio 3:5:7. If Brittany gives Alex half of her marbles, what's the total number of marbles that Alex has?

How many marbles are there in total? ** The total ratio representing the number of marbles is 3+5 +7 =

<<3+5+7=15>>15 How many marbles does Brittany have? ** From the ratio, the fraction representing the number of marbles that Brittany has is 3/15, which is equal to 3/15*600 = <<3/15*600=120>>120 marbles. How many marbles does Alex have? ** Alex has 5/15*600 = <<5/15*600=200>>200 marbles. How many marbles does Alex receive? ** If Brittany gives half of her marbles to Alex, Alex receives 1/2*120 = 60 marbles. What is the total number of marbles that Alex has? ** After receiving 60 marbles from Brittany, Alex has 200+60 = <<200+60=260>>260 marbles. #### 260 Connor wanted to order some new books to read. The website was offering free shipping over $50.00. They also had a deal that when you buy 4 books; the first two were 25% off. Book 1 cost 13.00 and Book 2 cost 15.00. Book 3 & 4 were both $10.00 each. How much more money did Connor need to spend to receive free shipping? How much did books 1 and 2 cost? ** Book 1 was $12.50 and book 2 was $15.00 so 13.00 +15.00 = $28.00 How much did books 1 and 2 cost after the 25% discount? ** He was buying 4 books, so these 2 were 25% off so 28.00 * .25 = $7.00 How much did books 1 and 2 cost after the 25% discount? ** These two books came out to 28-7 = $<<28-7=21.00>>21.00 How much did books 3 and 4 cost? ** Books 3 & 4 were both $10 each so 2*10 = $20.00 How much did books 1-4 cost? ** When you add all 4 books together, 21+20 = $<<21+20=41.00>>41.00 How much more money did Connor need to spend to receive free shipping? ** To get free shipping he would need to spend 50-41 = $<<50-41=9.00>>9.00 more on books #### 9 Victor has 8 flower stickers. He has 2 fewer animal stickers than flower stickers. How many stickers does Victor have in total? How many animal stickers does Victor have? ** Victor has 8 stickers - 2 stickers = <<8-2=6>>6 animal stickers How many stickers does Victor have in total? ** In total Victor has 8 stickers + 6 stickers = <<8+6=14>>14 stickers #### 14 Trish likes to go for walks every day. One day, she goes on a 1-mile walk. Every subsequent day, she doubles the distance she walked the previous day. On what day does she walk more than 10 times further than she did on the first day? How many miles does Trish walk on the second day? ** Trish walks 1 mile on the first day, and since she walks double the previous day's amount each day that means she walks 1*2=<<1*2=2>>2 miles the second day. How many miles does Trish walk on the third day? ** On the following day, she walks double the distance of the previous day's total of 2 miles, meaning she walks 2*2=<<2*2=4>>4 miles that day. How many miles does Trish walk on the fourth day? ** On the following day, she walks double the distance of the previous day's total of 4 miles, meaning she walks 4*2=<<4*2=8>>8 miles that day. How many miles does Trish walk on the fifth day? ** On the following day, she walks double the distance of the previous day's total of 8 miles, meaning she walks 8*2=<<8*2=16>>16 miles that day. What is the first day that Trish walks more than 10 times further than she did on the first day? ** As we're looking for the first day that her distance exceeds 10 times her original total, that means we're seeking a mile total of greater than or equal to 10*1= <<10*1=10>>10 miles, What is the first day that Trish walks more than 10 times further than she did on the first day? ** Since she accomplished this on the 5th day of walking, the answer is <<5=5>>5. #### 5 Jake is from a conservative household so during lunch at school one day, he gave one-quarter of his feeding allowance to a hungry friend. If candies cost 20 cents apiece and Jake's feeding allowance is $4, how many candies can his friend purchase with the money Jake gave to him? How much money did Jake give to his friend? ** One quarter of $4 is (1/4)*$4 = $<<(1/4)*4=1>>1 How many cents is $1? ** $1 is equivalent to 100 cents How many candies can Jake's friend purchase with the money Jake gave to him? ** 20 cents will buy 1 candy so 100 cents will buy 100/20 = <<100/20=5>>5 candies #### 5 A boy runs 1.5 km in 45 minutes. What is his speed in kilometers per hour? How many minutes are in 45 minutes? ** Since 1 hour is equal to 60 minutes, then 45 minutes is equal to 45/60 = <<45/60=0.75>>0.75 hours. What is his speed in kilometers per hour? ** Then, the speed in kilometers per hour is 1.5 km/0.75 hour = 2 kilometers per hour. #### 2 There are three buckets full of oranges. There are 22 oranges in the first bucket, 17 more oranges in the second bucket and 11 fewer oranges in the third bucket than in the second. How many oranges are there in all the buckets? How many oranges are in the second bucket? ** There are 22 + 17 = <<22+17=39>>39 oranges in the second bucket. How many oranges are in the third bucket? ** There are 39 - 11 = <<39-11=28>>28 oranges in the third bucket. How many oranges are there in all the buckets? ** There's a total of 22 + 39 + 28 = <<22+39+28=89>>89 oranges in the three buckets. #### 89 Chalktown High School had their prom last weekend. There were 123 students who attended. If 3 students attended on their own, how many couples came to the prom? How many students were in couples? ** There were 123 students – 3 single attendees = <<123-3=120>>120 students in couples. How many couples were there? ** 120 students / 2 in a couple = <<120/2=60>>60 couples. #### 60 Mancino is tending 3 gardens that each measure 16 feet by 5 feet. His sister, Marquita, is tilling the soil for two gardens that each measure 8 feet by 4 feet. How many square feet combined are in all their gardens? How many square feet in Mancino's gardens? ** 3 * (16 * 5) = <<3*(16*5)=240>>240 square feet How many square feet in Marquita's gardens? ** 2 * (8 * 4) = <<2*(8*4)=64>>64 square feet How many square feet combined are in all their gardens? ** 240 + 64 = <<240+64=304>>304 square feet How many square feet combined are in all their gardens? ** The gardens have a total of 304 square feet. #### 304