Answer:
(24) 3 - 4b = 10c + 10
(25) 4(3c+5) = 8
(26) - 6
(27) 4
Step-by-step explanation:
These questions require that words are translated into equations and then may be solved.
<u>(</u>24) Three minus four times a number is equal to ten times a number plus ten.
let the first number be b.
<em>(a)Three minus four times a number ... </em>can be represented as:
3 - (4 x b) = 3 - 4b
<em>(b) </em>...<em>ten times a number plus 10</em>
let the other number be c. Therefore we have;
(10 x c) + 10 = 10c + 10
Now, <em>three minus four times a number</em><em> is equal to </em><em>ten times a number plus ten </em>means that expressions in (a) and (b) above are equal. i.e
3 - 4b = 10c + 10
<u>(</u>25<u>)</u> Four times the quantity of three times c plus 5 is equal to 8.
<u>(</u>a) <em>four times the quantity of three times c plus 5</em> can be represented as
4 x (3 x c + 5) = 4(3c + 5)
(b) ... <em>is equal to 8. </em>This means that the expression in (a) is equal to 8.
4(3c + 5) = 8
(26) Six less than two thirds of a number is negative ten. Find the number.
(a) <em>six less than </em>can be represented as:
- 6
<em>(b) two thirds of a number </em> can be represented as
()x [where x is the number]
(c) <em>six less than two thirds of a number</em> can thus be written as;
()x - 6
(d) <em>... is negative 10 </em>means that the expression is (c) above is equal to -10. i.e
()x - 6 = -10
(e) Find the number.
The number can be found by solving for x in the expression in (d) above.
()x - 6 = -10 [multiply through by 3]
2x - 18 = -30 [collect like terms]
2x = -30 + 18
2x = -12 [divide both sides by 2]
x = - 6
Therefore, the number is -6
(27) Twenty-nine is thirteen added to four times a number. What is the number.
(a) <em>... thirteen added to four times a number</em> can be written as:
13 + 4b [where the number is b]
(b) <em>Twenty-nine is thirteen added to four times a number </em>means that the 29 is equal to the expression in (a) above. i.e
29 = 13 + 4b
(c) Find the number.
The number can be found by solving for b in the expression in (b) above. i.e
29 = 13 + 4b [collect like terms]
4b = 29 - 13
4b = 16 [divide both sides by 4]
b = 4
Therefore, the number is 4.