Determine the percentage increase in total students on the honor roll given 19% more boys and 20% more girls.
STEP 1
Assumptions1. Last year, the number of boys on the honor roll was100. Last year, the number of girls on the honor roll was503. This year, the number of boys on the honor roll increased by19%
4. This year, the number of girls on the honor roll increased by20%
STEP 2
First, we need to find the total number of students on the honor roll last year. This is the sum of the number of boys and girls on the honor roll.
Totallastyear=Numberofboyslastyear+Numberofgirlslastyear
STEP 3
Now, plug in the given values for the number of boys and girls last year to calculate the total number of students on the honor roll last year.
Totallastyear=100+50
STEP 4
Calculate the total number of students on the honor roll last year.
Totallastyear=100+50=150
STEP 5
Next, we need to find the number of boys and girls on the honor roll this year. This is done by increasing the number of boys and girls last year by their respective percentages.
Numberofboysthisyear=Numberofboyslastyear+(NumberofboyslastyeartimesIncreasepercentageofboys)Numberofgirlsthisyear=Numberofgirlslastyear+(NumberofgirlslastyeartimesIncreasepercentageofgirls)
STEP 6
Plug in the given values for the number of boys and girls last year and their increase percentages to calculate the number of boys and girls this year.
Numberofboysthisyear=100+(100times19%)Numberofgirlsthisyear=50+(50times20%)
STEP 7
Calculate the number of boys and girls on the honor roll this year.
Numberofboysthisyear=100+(100times0.19)=119Numberofgirlsthisyear=50+(50times0.20)=60
STEP 8
Now, we need to find the total number of students on the honor roll this year. This is the sum of the number of boys and girls on the honor roll this year.
Totalthisyear=Numberofboysthisyear+Numberofgirlsthisyear
STEP 9
Plug in the calculated values for the number of boys and girls this year to calculate the total number of students on the honor roll this year.
Totalthisyear=119+60
STEP 10
Calculate the total number of students on the honor roll this year.
Totalthisyear=119+60=179
STEP 11
Finally, we need to find the percentage increase in the total number of students on the honor roll. This is done by subtracting the total number of students last year from the total number this year, dividing by the total number last year, and then multiplying by100 to convert to a percentage.
Percentageincrease=((Totalthisyear−Totallastyear)/Totallastyear)times100
STEP 12
Plug in the calculated values for the total number of students this year and last year to calculate the percentage increase.
Percentageincrease=((179−150)/150)times100
STEP 13
Calculate the percentage increase.
Percentageincrease=((179−150)/150)times100=19.3%The total number of students on the honor roll increased by19.3%.