Homework Sourse3 One number is 2 more than 5 times another Their product is
3) One number is 2 more than 5 times another. Their product is 72. Find the numbers.
Set 1: (lower values)
(smaller value)
(larger value)
Set 2: (higher values)
(smaller value)
(larger value)
4) One number is 5 times another. Their product is 5 times their sum. Find the numbers.
Set 1: (lower values)
(smaller value)
(larger value)
Set 2: (higher values)
(smaller value)
(larger value)
10) If the total profit P of manufacturing x hundred items is given by the equation
P = 1300 + 800x 100x2,
find x when P is $2,500.
items (smaller value)
items (larger value)
Solution
3) Let greater number be x and other be y
Given: x=5y+2 ...........(i)
x*y=72 ...........(ii)
Using x from (i) and putting in (ii)
(5y+2)(y)=72
=>5y2+2y=72=>5y2+2y-72=0=>5y2+20y-18y-72=0=>5y(y+4)-18(y+4)=0=>(5y-18)(y+4)=0
=>y=18/5 or -4
For y=18/5, x=5(18/5)+2=20
for y=-4, x=5(-4)+2=-18
4)Let greater number be x and other be y
Given: x=5y ..........(i)
x*y=5(x+y) .............(ii)
Using value of x from (i) in (ii)
5y*y=5(5y+y)
5y2=30y=>5y2-30y=0=>5y(y-6)=0
=>y=0 or 6
for y=0, x=0
for y=6, x=30
10)P=1300+800x-100x2
for P=$2,500, putting this value of P in above equation
2500=1300+800x-100x2
1200-800x+100x2=0=>x2-8x+12=0=>x2-6x-2x+12=0=>x(x-6)-2(x-6)=0=>(x-2)(x-6)=0
=>x=2 or 6
