If two piles of toys added together make 120 toys in total, and the larger of the two piles is twice as big as the smaller one, how many toys are in the larger pile?

How many toys are in the smaller pile? ** First, we set up the equation 3x=120, dividing both sides by three to find that x=40

How many toys are in the larger pile? ** Then we multiply X by 2 to find that 40*2=

<<40*2=80>>80 How many toys are in the larger pile? ** As 80/2=40, and 40+80=<<120=120>>120, we find the sizes of the two piles as the larger pile is twice as big as the smaller pile, confirming that 80 is the answer. #### 80 Monica charges $25.00 per person when catering a dinner party. For repeat customers, she offers a 10% discount. Phoebe is a repeat customer who is having a dinner party for 20 guests. How much will Monica make from the party? How much does Monica charge? ** Phoebe is having 20 guests and Monica charges $25.00 per person so that’s 20*25 = $<<20*25=500.00>>500.00 How much does Phoebe get off? ** Phoebe is a repeat customer so she gets 10% off of $500.00 so that’s .10*500 = $<<10*.01*500=50.00>>50.00 discount How much will Monica make? ** Monica is charging $500.00 minus the repeat customer discount of $50.00 so she will make 500-50 = $<<500-50=450.00>>450.00 #### 450 The Diving Club offers 2 beginning diving classes on weekdays and 4 beginning classes on each day of the weekend. Each class has room for 5 people. How many people can take classes in 3 weeks? How many classes are there on weekdays? ** There are 2 classes x 5 days = <<2*5=10>>10 classes on weekdays. How many classes are there on weekends? ** There are 4 classes x 2 days = <<4*2=8>>8 classes on weekends. How many classes are there in total? ** There are a total of 10 + 8 = <<10+8=18>>18 classes per week. How many people can take classes in 3 weeks? ** So each week, 18 x 5 = <<18*5=90>>90 people can take classes. How many people can take classes in 3 weeks? ** Thus, 90 x 3 = <<90*3=270>>270 people can take classes in 3 weeks. #### 270 The total average age of three friends is 40. Jared is ten years older than Hakimi, and Molly's age is 30. How old is Hakimi? How old are the three friends? ** The total age for the three friends is 40*3 = <<40*3=120>>120 How old are Jared and Hakimi? ** If Molly's age is 30, then Jared and Hakimi have a total age of 120-30 = 90. Define a variable ** Let's say the age of Hakimi is x. How old is Jared? ** Since Jared is 10 years older than Hakimi, Jared is x+10 years old. How old are Jared and Hakimi? ** Jared and Hakimi's total age is x+(x+10) = 90 Write an equation ** This translates to 2x=90-10 Simplify ** 2x=80 Divide by 2 ** Hakimi's age is x=80/2 How old is Hakimi? ** This gives us x=<<40=40>>40, which is Hamkimi's age. #### 40 Martin rings the small bell 4 times more than 1/3 as often as the big bell. If he rings both of them a combined total of 52 times, how many times does he ring the big bell? How many times does Martin ring the small bell? ** Let s be the number of times the small bell rings, and b be the number of times the big bell rings. We know that s + b = 52 and s = 4 + 1/3b. How many times does Martin ring the big bell? ** Substituting the second equation into the first equation, we get 4 + 1/3b + b = 52 How many times does Martin ring the big bell? ** Subtracting 4 from both sides, we get 1/3b + b = 48 How many times does Martin ring the big bell? ** Combining like terms, we get 4/3b = 48 How many times does Martin ring the big bell? ** Dividing both sides of the equation by 4/3, we get b = 36 #### 36 Sabrina is collecting herbs to make a poultice for her grandmother. She needs twice as many basil leaves as sage leaves and 5 fewer sage leaves than verbena leaves. If she needs 12 basil leaves, how many leaves total does she need? How many sage leaves does Sabrina need? ** First find the number of sage leaves Sabrina needs: 12 basil / 2 basil/sage = <<12/2=6>>6 sage How many verbena leaves does Sabrina need? ** Then add 5 to find the total number of verbena leaves she needs: 6 sage + 5 = <<6+5=11>>11 verbena How many leaves total does Sabrina need? ** Finally, add up all the different leaves to find the total number: 6 sage + 11 verbena + 12 basil = <<6+11+12=29>>29 leaves #### 29 Ruel has four books of 10 stamps and six books of 15 stamps. How many stamps does Ruel have? How many stamps does Ruel have from the four books? ** Ruel has a total of 4 x 10 = <<4*10=40>>40 stamps from the four books. How many stamps does Ruel have from the six books? ** He also has 6 x 15 = <<6*15=90>>90 stamps from the six books. How many stamps does Ruel have? ** Therefore, he has a total of 40 + 90 = <<40+90=130>>130 stamps. #### 130 Madeline has 10 flowers. If 4 flowers are red, 2 flowers are white, and the rest are blue, what percentage of flowers are blue? How many flowers are not blue? ** There are 4+2 = <<4+2=6>>6 flowers that are not blue. How many flowers are blue? ** Thus, there are 10-6 = <<10-6=4>>4 blue flowers. What percentage of flowers are blue? ** Thus, blue flowers make up (4/10)*100=<<4/10*100=40>>40%. #### 40 For the school play, 40 rows of chairs were set up where there were 20 chairs in each row. If only 10 seats were not occupied, how many seats were taken? How many chairs were set up? ** The school prepared 40 x 20 = <<40*20=800>>800 chairs. How many chairs were taken? ** So, 800 - 10 = <<800-10=790>>790 chairs were taken. #### 790 Apple can run at a rate of 3 miles per hour. Mac can run at a rate of 4 miles per hour. In minutes, how much faster will Mac run a 24 mile race? How many hours does it take Apple to run 24 miles? ** First find how fast each runs. Apple = 24 miles / 3 miles per hour = <<24/3=8>>8 hours How many hours does it take Mac to run 24 miles? ** Mac = 24 miles / 4 miles per hour = <<24/4=6>>6 hours. How many hours faster will Mac run a 24 mile race? ** Mac runs 8 hours - 6 hours = <<8-6=2>>2 hours faster. How many minutes faster will Mac run a 24 mile race? ** 1 hour = 60 minutes, so, Mac runs faster by 2 hours * 60 minutes = <<2*60=120>>120 minutes. #### 120