Write an equation for the following questions:
a) $3$ times a number x is added to $5$ times another number y is equals to $48$ .
b) Sum of squares of three number is $83$ .
c) Difference of squares of two numbers m and n (m $>$ n) is $56$ .
d) A number divided by $5$ gives $7$ less than twice of the number.

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Solution

a) $3 x + 5 y = 48$
b) Let the numbers be x, y, z.
$x^{2} + y^{2} + z^{2} = 83$
c) $m^{2} - n^{2} = 56$
d) Let the number be x.
$\frac{x}{5} = 2 x - 7$

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Similar questions

Q. Write each of the following statements as an equation:
(i) 5 times a number equals 40.
(ii) A number increased by 8 equals 15.
(iii) 25 exceeds a number by 7.
(iv) A number exceeds 5 by 3.
(v) 5 subtracted from thrice a number is 16.
(vi) If 12 is subtracted from a number, the result is 24.
(vii) Twice a number subtracted from 19 is 11.
(viii) A number divided by 8 gives 7.
(ix) 3 less than 4 times a number is 17.
(x) 6 times a number is 5 more than the number.

Question 85

Translate each of the following statement into an equation, using x as the variable.

(a) 13 subtracted from twice a number gives 3.

(b) One-fifth of a number is 5 less than that number.

(d) 9 added to twice a number gives 13.

(e) 1 subtracted from one-third of a number gives 1.

Q. Frame equations for the given statements:

S.No.	Statement	Equation
(a)	4 subtracted from 7 times $a$ gives 32.
(b)	3 is 7 more than two-fifth of $y$ .
(c)	The number $b$ divided by 5 gives 6.
(d)	8 times a number $x$ is equal to three more than 5 times the same number.
(e)	3 less than 4 times a number $p$ is 5 more than twice the same number.

[5 marks]

Write an equation for each of the following statements :

$3$ times a number $x$ added to $5$ times another number $y$ is equal to $48 .$

Match Column I with Column II in the following:

$\begin{matrix} C o l u m n I & C o l u m n I I 1. & T h e d i f f e r e n c e o f 3 a n d a n u m b e r & (a) & 4 - 2 x s q u a r e d 2. & 5 l e s s t h a n t w i c e a n u m b e r s q u a r e d & (b) & n^{2} - 3 3. & F i v e m i n u s t w i c e t h e s q u a r e o f a & (c) & 2 n^{2} - 5 n u m b e r 4. & F o u r m i n u s a n u m b e r m u l t i p l i e d b y 2 & (d) & 5 - 2 n^{2} 5. & S e v e n t i m e s t h e s u m o f a n u m b e r a n d 1 & (e) & 3 - n^{2} 6. & A n u m b e r s q u a r e d p l u s 6 & (f) & 2 (n + 6) 7. & 2 t i m e s t h e s u m o f a n u m b e r a n d 6 & (g) & 7 (n + 1) 8. & T h r e e l e s s t h a n t h e s q u a r e o f a n u m b e r & (h) & n^{2} + 6 \end{matrix}$

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Write an equation for the following questions:a) 3 times a number x is added to 5 times another number y is equals to 48.b) Sum of squares of three number is 83.c) Difference of squares of two numbers m and n (m>n) is 56.d) A number divided by 5 gives 7 less than twice of the number.

a)3x+5y=48b) Let the numbers be x, y, z.x2+y2+z2=83c) m2-n2=56d) Let the number be x.x5=2x-7

a) $3 x + 5 y = 48$
b) Let the numbers be x, y, z.
$x^{2} + y^{2} + z^{2} = 83$
c) $m^{2} - n^{2} = 56$
d) Let the number be x.
$\frac{x}{5} = 2 x - 7$