. Translate the English sentence into an equation using the givenvariables. a) K
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Question
. Translate the English sentence into an equation using the givenvariables.
a) Kerri’sapartment building has 6 more floors than Eric’sbuilding. Use k for the number of floors in Kerri’sbuilding and e for the number of floors in Eric’sbuilding.
b) The temperatureon Friday showed a decrease of 5 degrees compared to thetemperature two days before on Wednesday. Use f for the numberof degrees on Friday and w for the number of degrees onWednesday.
c) The length of arectangle is 3 centimeters greater than five times thewidth. Use L for the length and W for the width of therectangle.
d) The length ofthe second side of a triangle is 8 inches shorter than twice thefirst side of the triangle. Use f to represent the length ofthe first side of the triangle and s to represent the length of thesecond side of the triangle.
2. Write algebraicexpressions for each quantity using the given variable.
a) Rasheed’smonthly salary is $100 more than Fred’s monthlysalary. Use the letter f.
b) Lake Regina has190,000 fewer square feet of surface area than LakeMontrose.
Use the letter m.
c) The second angleof a triangle is smaller than the first. The third angleis triple the size of the first angle. Use the letter f.
3. Solve thefollowing comparison problems using an equation.
a) A 22-ft pipe iscut into two pieces. The shorter piece is 7 ft shorter thanthe longer piece. What is the length of the longer piece?
b) For three daysin a row, volunteers picked up trash on a particularbeach. They picked up a total of 813 pounds. On thesecond day they collected 15 pounds more than on the firstday. On the third day, they picked up 27 pounds less than onthe first day. How many pounds of trash did they pick up onthe first day?
4. Solve thefollowing geometric concept problems using an equation.
a) To trim theedges of a rectangular table cloth, 36 feet of lace areneeded. The width of the table cloth is exactly one-half itslength. What are the dimensions of the table cloth?
b) A triangle hasthree angles, R, S, and T. Angle T is 18° greater thanangle S. Angle R is 4 times angle S. What is the measureof each angle?
5. Solve thefollowing rate/percent problems.
a) A salesman in anexclusive clothing store earns $2300 per month base pay plus a 7%commission on sales. One month he earns $5023. What werehis sales that month?
b) The number ofdogs licensed in a particular city this year is 1283. This isa 2% increase over last year. How many dog licenses were onrecord last year? Round to the nearest whole number.
. Translate the English sentence into an equation using the givenvariables.
a) Kerri’sapartment building has 6 more floors than Eric’sbuilding. Use k for the number of floors in Kerri’sbuilding and e for the number of floors in Eric’sbuilding.
b) The temperatureon Friday showed a decrease of 5 degrees compared to thetemperature two days before on Wednesday. Use f for the numberof degrees on Friday and w for the number of degrees onWednesday.
c) The length of arectangle is 3 centimeters greater than five times thewidth. Use L for the length and W for the width of therectangle.
d) The length ofthe second side of a triangle is 8 inches shorter than twice thefirst side of the triangle. Use f to represent the length ofthe first side of the triangle and s to represent the length of thesecond side of the triangle.
2. Write algebraicexpressions for each quantity using the given variable.
a) Rasheed’smonthly salary is $100 more than Fred’s monthlysalary. Use the letter f.
b) Lake Regina has190,000 fewer square feet of surface area than LakeMontrose.
Use the letter m.
c) The second angleof a triangle is smaller than the first. The third angleis triple the size of the first angle. Use the letter f.
3. Solve thefollowing comparison problems using an equation.
a) A 22-ft pipe iscut into two pieces. The shorter piece is 7 ft shorter thanthe longer piece. What is the length of the longer piece?
b) For three daysin a row, volunteers picked up trash on a particularbeach. They picked up a total of 813 pounds. On thesecond day they collected 15 pounds more than on the firstday. On the third day, they picked up 27 pounds less than onthe first day. How many pounds of trash did they pick up onthe first day?
4. Solve thefollowing geometric concept problems using an equation.
a) To trim theedges of a rectangular table cloth, 36 feet of lace areneeded. The width of the table cloth is exactly one-half itslength. What are the dimensions of the table cloth?
b) A triangle hasthree angles, R, S, and T. Angle T is 18° greater thanangle S. Angle R is 4 times angle S. What is the measureof each angle?
5. Solve thefollowing rate/percent problems.
a) A salesman in anexclusive clothing store earns $2300 per month base pay plus a 7%commission on sales. One month he earns $5023. What werehis sales that month?
b) The number ofdogs licensed in a particular city this year is 1283. This isa 2% increase over last year. How many dog licenses were onrecord last year? Round to the nearest whole number.
Explanation / Answer
1) a) Kerri’s apartment building has 6 more floorsthan Eric’s building. Use k for the number of floors inKerri’s building and e for the number of floors inEric’s building.K=E+6
b) The temperature on Friday showed adecrease of 5 degrees compared to the temperature two days beforeon Wednesday. Use f for the number of degrees on Friday and wfor the number of degrees on Wednesday. F=W-6 c) The length of a rectangle is 3centimeters greater than five times the width. Use L for thelength and W for the width of the rectangle. L=3+5W
d) The length of the second side of atriangle is 8 inches shorter than twice the first side of thetriangle. Use f to represent the length of the first side ofthe triangle and s to represent the length of the second side ofthe triangle. S=2F-8
2. a) Rasheed’s monthlysalary is $100 more than Fred’s monthly salary. Use theletter f. R=100+F b) Lake Regina has 190,000 fewersquare feet of surface area than Lake Montrose. Use the letterm.
R=M-190000
c) The second angle of atriangle is smaller than the first. The third angle istriple the size of the first angle. Use the letter f. T=third S=second F=first T=3F 3. Solve the following comparison problems using anequation.
a) A 22-ft pipe is cut into twopieces. The shorter piece is 7 ft shorter than the longerpiece. What is the length of the longer piece? s=shorter piece l=longer piece s=l-7 b) For threedays in a row, volunteers picked up trash on a particularbeach. They picked up a total of 813 pounds. On thesecond day they collected 15 pounds more than on the firstday. On the third day, they picked up 27 pounds less than onthe first day. How many pounds of trash did they pick up onthe first day? s=second day f=first day t=third day s=15+f
t=f-27 s+f+t=813 (15+f)+f+(f-27)=813 15+3f-27=813 -12+3f=813 3f=825 f=275 4. Solve the following geometric conceptproblems using an equation. a) To trim the edges of arectangular table cloth, 36 feet of lace are needed. The widthof the table cloth is exactly one-half its length. What arethe dimensions of the table cloth? W=1/2L Perimeter: 2W+2L=36 2(1/2L)+2L=36 L+2L=36 3L=36 L=12 W=1/2(12) W=6 b) A triangle has three angles,R, S, and T. Angle T is 18° greater than angleS. Angle R is 4 times angle S. What is the measure ofeach angle?
A triangle is 180 degrees. T=18+S R=4S R+S+T=180 (4S)+S+(18+S)=180 6S+18=180 6S=168 S=28 R=4(28)=112 T=18+28=46 5. Solve the following rate/percent problems. a) A salesman in anexclusive clothing store earns $2300 per month base pay plus a 7%commission on sales. One month he earns $5023. What werehis sales that month? Earns 2300+.07(x) x=5023 Total=2300+.07(5023) Total=$2651.61 b) The number of dogs licensedin a particular city this year is 1283. This is a 2% increaseover last year. How many dog licenses were on record lastyear? Round to the nearest whole number.
Last year = x r=.02 This one, I totally forgot. When I did problems similar tothese on the SATs, I just plugged and chugged.
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