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(i) 10 students of class X took part in a mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
(ii) 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen.
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(i) Let number of boys = x
Let number of girls = y
According to given conditions, we have
x + y = 10
And, x = 10 - y
putting y=0,5,10,we get,
X=10-0=10
X=10-5=5,
X=10-10=0
x | 10 | 5 | 0 |
y | 0 | 5 | 10 |
Number of girls is 4 more than number of boys ........Given,
so,
Y=x+4
putting x=-4,0,4 we get,
Y=-4+4=0
Y=0+4
Y=4+4=8
x | -4 | 0 | 4 |
y | 0 | 4 | 8 |
(ii) Let the cost of one pencil=Rs.X
and Let the cost of one pen=Rs.Y
According to the given conditions, we have:
=5x + 7y = 50
=5x=50-7y
=x=10-7/5y
x | 3 | -4 | -11 |
y | 5 | 10 | 15 |
Now,
7 pencils and 5 pens together cost Rs. 46
7x + 5y = 46
= 5y = 46 – 7x
= y = 9.2 – 1.4x
Putting x = 0 , 2 , 4 we get,
Y= 9.2 – 1.4×0 = 9.2
Y = 9.2 – 1.4 × 2 = 9.2 – 2.8 = 6.4
Y = 9.2 – 1.4 × 4 = 9.2 – 5.6 = 3.6
x | 0 | 2 | 4 |
y | 9.2 | 6.4 | 3.6 |
The graphical representation is as follows:
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