Sheet # 84
Name: ________________________ Date_____________
Explain and Show Your Work.
1) Two times an integer is 8 more than 4 times the next consecutive integer. What are the two integers?
2) Suppose a rectangle is 2 inches longer than it is wide and its perimeter is 76 inches. Find the length of the long side of the rectangle.
3) Misha is now 3 years older than Tanya. If in 12 years, the sum of their ages will be 61, how old is Tanya now?
4) Jody earns $150 more per month than Frank. If there monthly salaries total $4350, what amount does each earn?
5) The sides of a triangle are consecutive integers. If the perimeter of the triangle is 48 cm, how long is each side?
Answers for sheet # 84
1) n is the first integer. Next integer is n + 1
2n= 4(n+1) + 8
2n = 4n + 4 + 8
2n = 4n + 12
2n = - 12
n = - 6
next integer = - 6 + 1 = - 5
2) Length = L
Width = W
L = W + 2
Perimeter
2L + 2W = 76
2(W + 2) + 2W = 76
2W + 4 + 2W = 76
4W + 4 = 76
4W = 72
W = 18 cm
L = 18 + 2 = 20 cm
3) Misha's Age = M
Tanya's Age = T
M = T + 3
In 12 years, Misha's age will be M + 12
In 12 year, Tanya's age will be T + 12
(M + 12) + (T + 12) = 61
M + T + 24 = 61
From above, replace M with T + 3
T + 3 + T+ 24 = 61
2T + 27 = 61
2T = 34
T = 17 years
Tanya's age is 17 years.
Misha's is 17 + 3 = 20 years ( M = T + 3)
4) Jody's salary = j
Frank's salary = f
j = f + 150
j + f = 4350
f + 150 + f = 4350
2f + 150 = 4350
2f = 4200
f = 2100
Frank's salary = $2100
Jody's salary = $2100 + $150 = $2250
5)
First side = n
Second side = n + 1
Third side = n + 2
Perimeter of the triangle = (n) + (n+1) + (n+2) = 48
3n + 3 = 48
3n = 45
n = 15 cm
first side = 15 cm
second side = 16 cm
third side = 17 cm