Ken bought some pencils and rulers from a shop. Each pencil cost $0.70 and each ruler cost $0.40. Ken bought 7 more rulers than pencils but spent $1.10 less on the rulers than on the pencils.
(a) How many pencils did Ken buy?
(b) How much money did Ken spend on the rulers?
(a)
Let the number of pencils bought be x
Ruler=x+7
cost of pencils=0.7x
cost of rulers= 0.4(x+7)=0.4x+2.8
0.4x+2.8=0.7x-1.1
2.8+1.1=0.7x-0.4x
3.9=0.3x
x=13
number of pencils bought= 13
(b)
number of rulers bought=13+7=20
cost=20(0.40)
=$8.00
Let's assume the number of pencils Ken bought is "x".
(a) Since Ken bought 7 more rulers than pencils, the number of rulers he bought is "x+7".
The cost of pencils is $0.70 each, so Ken spent 0.70x dollars on pencils.
The cost of rulers is $0.40 each, so Ken spent 0.40(x+7) dollars on rulers.
(b) According to the given information, Ken spent $1.10 less on the rulers than on the pencils.
Therefore, we can set up the equation:
0.70x - 1.10 = 0.40(x + 7)
Let's solve this equation step by step:
0.70x - 1.10 = 0.40x + 2.80
Subtract 0.40x from both sides:
0.30x - 1.10 = 2.80
Add 1.10 to both sides:
0.30x = 3.90
Now, divide both sides by 0.30 to solve for x:
x = 13
So, Ken bought 13 pencils.
To find out how much money Ken spent on the rulers, substitute the value of x (13) into the equation:
Cost of rulers = 0.40(x + 7)
= 0.40(13 + 7)
= 0.40(20)
= $<<0.40*20=8>>8
Therefore, Ken spent $8 on the rulers.