Hadley loves to do volunteer work at the local library. On a certain day, she neatly arranges 100 books on the shelf. By lunchtime, a certain number of books had been borrowed. She added 40 more books to the same shelf. By evening, 30 more books had been borrowed. If the shelf had 60 books remaining by the evening, how many books had been borrowed by lunchtime?

Define a variable ** Let x be the number of books borrowed by lunchtime.

How many books are remaining? ** So by lunchtime, the remaining number of books will be 100-x

How many books are remaining after adding 40 more books? ** After adding 40 more books, the total number of books increased to 100-x+40.

How many books are remaining by evening? ** By evening, after 30 more books have been borrowed, the total number of books remaining is 100-x+40-30 = 60

Write an equation ** Thus 110 - x = 60.

Divide by 10 ** Thus x =

<<50=50>>50 books #### 50 We the People has 17 cows. Happy Good Healthy Family has two more than three times the number of cows We the People has. If their cows are taken to a ranch to graze together, how many cows will be in the ranch altogether? How many cows does Happy Good Healthy Family have? ** Three times the number of cows We the People has is 3*17=<<3*17=51>>51 cows. How many cows does Happy Good Healthy Family have? ** Happy Good Healthy Family has two more than three times the number of cows We the People has, a total of 51+2=53 cows. How many cows will be in the ranch altogether? ** If the cows are taken to a ranch to graze together, their total will be 53+17=<<53+17=70>>70 cows. #### 70 Coleen loved sprinkles. At the beginning of the day, she had twelve cans of sprinkles. After applying sprinkles to her hair, her clothing and her pets, she had 3 less than half as many cans of sprinkles as she started out with. How many cans of sprinkles remained? How many cans of sprinkles are there? ** Half of twelve cans of sprinkles is 12/2=<<12/2=6>>6 cans. How many cans of sprinkles remain? ** Three less than half as many cans of sprinkles is 6-3=<<6-3=3>>3 cans of sprinkles. #### 3 Beth had 150 students in her 10th-grade class. The following year 30 more students join. In her final year, 15 students left. How many students did Beth have in her class at the end of her final year? How many students did Beth have in her 10th-grade year? ** Beth had 150 students her 10th-grade year, and added 30 more the following for a total of 150+30= <<150+30=180>>180 students How many students did Beth have in her class at the end of her final year? ** In her final year, 15 students left her class, bringing her total to 180-15=165 students #### 165 Harper drinks a 1/2 bottle of mineral water per day. She buys the mineral water by the case at a big box store. They come 24 bottles to a case and are currently on sale for $12.00. If she wants to buy enough cases to last her 240 days, how much will she spend? How many days will a case last? ** She drinks 1/2 bottle a day and there are 24 bottles in a case so a case will last 24/.5 = <<24/.5=48>>48 days How many cases will she need? ** She needs enough to last her 240 days and 1 case will last her 48 days so she needs 240/48 = <<240/48=5>>5 cases How much will each case cost? ** Each case is on sale for $12.00 and she needs 5 cases so that's 12*5 = $<<12*5=60.00>>60.00 #### 60 Estevan has 24 blankets. One-third of the blankets have polka-dots. For his birthday, his mother gives him 2 more polka-dot print blankets. How many polka-dot blankets does Estevan have in total? How many polka-dot blankets does Estevan have before his birthday? ** Before his birthday, Estevan has 24 / 3 = <<24/3=8>>8 polka-dot blankets How many polka-dot blankets does Estevan have after his birthday? ** After his birthday, Estevan has 8 + 2 = <<8+2=10>>10 polka-dot blankets #### 10 Lorenzo put three full cans of thumbtacks into his pocket and went off to work at the corkboard factory. It was Lorenzo's job, as head of quality control, to test every cork board for its ability to hold thumbtacks. He placed one thumbtack from each of the three cans of thumbtacks into every board tested. At the end of the day, he had tested 120 boards and had 30 tacks remaining in each of the three cans. What was the total combined number of thumbtacks from the three full cans? How many tacks did Lorenzo test? ** At the end of the day, he had tested 120 boards, each with three tacks, for a total of 3*120=<<120*3=360>>360 tacks How many tacks did Lorenzo have left? ** He had 30 tacks remaining in each of the three cans, for an additional 3*30=<<3*30=90>>90 thumbs tacks. What was the total combined number of thumbtacks from the three full cans? ** Therefore, the original total combined number of thumbtacks in the three full cans of thumbtacks was 360+90=<<360+90=450>>450 thumbtacks. #### 450 Janice adds 2 tablespoons of koolaid power and 16 tablespoons of water to a jug. She leaves it out long enough for 4 tablespoons of water to evaporate. Then she quadruples the amount of water in the jug. What percentage of the liquid in the jug is koolaid powder? How many tablespoons of water are left after the evaporation? ** First find how many tablespoons of water are left after the evaporation: 16 tbs - 4 tbs = <<16-4=12>>12 tbs How much water is in the jug after Janice refills it? ** Then multiply this number by 4 to find how much water is in the jug after Janice refills it: 12 tbs * 4 = <<12*4=48>>48 tbs How much liquid is in the jug? ** Now add the 2 tablespoons of koolaid powder to find the total volume of the liquid in the jug: 48 tbs + 2 tbs = <<48+2=50>>50 tbs What percentage of the liquid in the jug is koolaid powder? ** Now divide the volume of the koolaid powder by the total volume and multiply by 100% to find the percentage of the liquid that's koolaid: 2 tbs / 50 tbs * 100% = 4% #### 4 Ignatius owns 4 bicycles. A friend of his owns different types of cycles, which have three times are many tires as Ignatius's bikes have. He has one unicycle, a tricycle, and the rest are bikes. How many bicycles does the friend own? How many tires does Ignatius have? ** Ignatius has 8 tires because 2 x 4 = <<2*4=8>>8 How many tires does the friend have? ** His friend has 24 tires because 3 x 8 = <<3*8=24>>24 How many bicycle wheels does the friend have? ** There are 20 bicycle wheels because 24-1-3 = <<24-1-3=20>>20 How many bicycles does the friend have? ** He has 10 bicycles because 20 / 2 = <<20/2=10>>10 #### 10 Rory has 30 more jellybeans than her sister Gigi who has 15 jellybeans. Lorelai has already eaten three times the number of jellybeans that both girls have. How many jellybeans has Lorelai eaten? How many jellybeans does Rory have? ** Rory has 30 more jellybeans than Gigi who has 15 so Rory has 30+15 = <<30+15=45>>45 jellybeans How many jellybeans do Rory and Gigi have together? ** Rory has 45 jellybeans and Gigi has 15 so that's 45+15 = <<45+15=60>>60 jellybeans total How many jellybeans has Lorelai eaten? ** Lorelai has eaten three times the amount of jellybeans that both girls have so she has eaten 3*60 = <<3*60=180>>180 jellybeans #### 180