Respuesta :

Answer:

Ques 1)

A number  decreased by 32 is -58.

Let the number be 'x'.

i.e. x-32=-58

⇒ x= -58+32

⇒ x= -26.

Hence the number is -26.

Ques 2)

The product of 14 and n is -28.

The expression is:

⇒ 14n= -28

on solving we get:

n= -2 ( since on dividing both side by 14)

Ques 3)

Let the number be 'x'.

i.e. 4x=x+78

4x-x=78

3x=78

x=26.

Hence, the number is 26.

Ques 4)

Let the price of red bike is $ r.

so, the cost of blue bike is: $ (r-14)

also, r+r-14=300

2r-14=300

2r=314

r=157

Hence, the cost of red bike is: 157

and the cost of blue bike is: 143

Ques 5)

Let the age of Emma is: x years.

and the age of Alex is x+6 years.

Also,

x+x+6=32

2x+6=32

2x=32-6

2x=22

x=11.

Hence, age of Emma is 11 years.

and age of Alex is 17 years.

Ques 6)

Let age of Mousy is x years.

and age of Mrs. computer= 3x years.

Also,

x+3x=52

4x=52

x=13

Hence age of Mousy is 13 years.

and age of Mrs. Computer is 39 years.

Ques 7)

Let the age of Tom is x years.

so, the age of Mike is (2x+5) years.

Hence,

2x+5+x=65

3x+5=65

3x=60

x=20.

Hence, age of Tom is 20 years.

and age of Mike is: 2×20+5=45 years.

Ques 8)

Let the first integer is 'x'.

second integer is (x+1)

third integer is: (x+2)

Hence, the expression is given as:

(x+1)+(x+2)=17

Ques 9)

Let the first integer is 'x'.

second integer is (x+1)

third integer is: (x+2)

There sum is 108.

Hence,

x+x+1+x+2=108

3x+3=108

Ques 10)

Let the first odd integer is x

the next odd integer will be: x+2.

There sum is 72.

Hence,

x+x+2=72

i.e. 2x+2=72

kudzordzifrancis

QUESTION 1

Let the number be  [tex]x[/tex].

If this number is decreased by 32 and the result is -58, then we can write the following equation and solve for [tex]x[/tex].

[tex]x-32=-58[/tex].

Group the similar terms to get;

[tex]x=-58+32[/tex]

[tex]x=-26[/tex]

The number is -26.

QUESTION 2

The product of 14 and [tex]n[/tex] is [tex]14\times n=14n[/tex]

If the product is -28, then the require algebraic equation is

[tex]14n=-28[/tex]

QUESTION 3

Let the number be [tex]y[/tex].

Four times this number is [tex]4y[/tex].

The number increased by 78 is [tex]y+78[/tex].

If four times the number is the same as the number increased by 78, then we write and solve the equation;

[tex]4y=y+78[/tex]

Group the similar terms;

[tex]4y-y=78[/tex]

Simplify

[tex]3y=78[/tex]

Divide both sides by 3;

[tex]y=\frac{78}{3}[/tex]

[tex]y=26[/tex]

The number is 26

QUESTION 4

Let [tex]b[/tex] represent the price of the blue bike and [tex]r[/tex] represent the price of the red bike.

Then we can write the following two equations and solve simultaneously.

[tex]b=r-14...(1)[/tex]

[tex]b+r=300...(2)[/tex]

We substitute equation (1) into equation (2) to obtain;

[tex]r-14+r=300[/tex]

Group like terms;

[tex]r+r=300+14[/tex]

Simplify;

[tex]2r=314[/tex]

Divide both sides by 2

[tex]r=157[/tex]

The red bike is $157

and

The blue bike is 157-14=$143

QUESTION 5

Let [tex]a[/tex] represent the age of Alex and [tex]e[/tex] represent the age of his sister. Then;

[tex]a=e+6...(1)[/tex]

[tex]a+e=32..(2)[/tex]

Put equation (1) into equation (2) to get;

[tex]e+6+e=32[/tex]

[tex]\Rightarrow e+e=32-6[/tex]

[tex]\Rightarrow 2e=26[/tex]

[tex]\Rightarrow e=13[/tex]

Alex is 13+6=19 years old.

QUESTION 6

Let [tex]c[/tex] represent Mrs computer's age and [tex]m[/tex] represent Mousy's age. Then;

[tex]c=3m...(1)[/tex]

[tex]c+m=52...(2)[/tex]

Put equation (1) into equation (2).

[tex]\Rightarrow 3m+m=52[/tex]

[tex]\Rightarrow 4m=52[/tex]

[tex]\Rightarrow m=\frac{52}{4}[/tex]

[tex]\Rightarrow m=13[/tex]

Mousy is 13 years old.

QUESTION 7.

Let Mike be [tex]m[/tex] years and Tom be [tex]t[/tex] years.

Then;

[tex]m=2t+5...(1)[/tex]

[tex]m+t=65...(2)[/tex]

Put equation (1) into equation (2) and solve.

[tex]\Rightarrow 2t+5+t=65[/tex]

[tex]\Rightarrow 2t+t=65-5[/tex]

[tex]\Rightarrow 3t=60[/tex]

[tex]\Rightarrow t=\frac{60}{3}[/tex]

[tex]\Rightarrow t=20[/tex]

Mike is 2(20)+5=45 years old.

QUESTION 8

Let the consecutive integers be

[tex]x,x+1,x+2[/tex]

The sum of the second and third is 17 gives the equation;

[tex](x+1)+(x+2)=17[/tex]

The second choice is correct

QUESTION 9

Let the consecutive  integers be

[tex]x,x+1,x+2[/tex]

Their sum being 108 gives the equation

[tex]x+x+1+x+2=108[/tex]

Regroup

[tex]x+x+x+1+2=108[/tex]

Simplify the LHS

[tex]3x+3=108[/tex]

Factor the LHS

[tex]3(x+1)=108[/tex]

Correct choice is A

QUESTION 10

Let the two consecutive odd integers be;

[tex]x,x+2[/tex]

The sum being 72 gives the equation;

[tex]x+x+2=72[/tex]

Simplify the first two terms

[tex]2x+2=72[/tex]

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