All categories

2 years ago

The ages of three sisters are consecutive integers. The sum of their ages is 72. Calculate their ages.

Mathematics

1 answer:

Luda [366]2 years ago

6 0

Answer: 1st: 23 years old, 2nd: 24 years old, 3rd: 25 years old

Step-by-step explanation:

Let the ages a, b and c

a + b + c = 72

b = a + 1 (b is consecutive to a)

c = a + 2 (c is consecutive to b)

a + a + 1 + a + 2 = 72

3a +3 = 72

3a = 72-3 = 69

a = 69/3 = 23 years old, that is the 1st child's age

b = a + 1 = 24 years old, that is the 2nd child's age

c = a + 2 = 25 years old, that is the 3rd child's age

<h3>Verification</h3>

a + b + c= 23 + 24 + 25 = 72 years

$\textit{\textbf{Spymore}}$

You might be interested in

Isaac keeps track of the miles per gallon his car gets per week. He has accumulated the following data:

ipn [44]

we know that

A <u>geometric sequence</u> is a sequence of numbers in which the ratio between consecutive terms is constant

Let

$a1=24 \ a2=24.48\ a3=24.97\ a4=25.47$

$\frac{a2}{a1} = \frac{24.48}{24}= 1.02$

$a2=a1*1.02$

$\frac{a3}{a2} = \frac{24.97}{24.48}= 1.02$

$a3=a2*1.02$

$\frac{a4}{a3} = \frac{25.47}{24.97}= 1.02$

$a4=a3*1.02$

therefore

The common ratio is equal to $1.02$

<u>the answer is</u>

The common ratio is 1.02

4 0

2 years ago

Read 2 more answers

Unit 7 polygons & quadrilaterals homework 3: rectangles Gina Wilson answer key

Irina-Kira [14]

Answer:

In the image attached you can find the Unit 7 homework.

We need to findt he missing measures of each figure.

Notice that the first figure is a rectangle, which means opposite sides are congruent so,

VY = 19

WX = 19

YX = 31

VW = 31

To find the diagonals we need to use Pythagorean's Theorem, where the diagonals are hypothenuses.

$VX^{2}=19^{2}+31^{2}\\ VX=\sqrt{361+961}=\sqrt{1322} \\VX \approx 36.36$

Also, $YW \approx 36.36$ , beacuse rectangles have congruent diagonals, which intercect equally.

That means, $ZX = \frac{VX}{2} \approx \frac{36.36}{2}\approx 18.18$

Figure number two is also a rectangle.

If GH = 14, that means diagonal GE = 28, because diagonals intersect in equal parts.

Now, GF = 11, because rectangles have opposite sides congruent.

DF = 28, because in a reactangle, diagonals are congruent.

HF = 14, because its half of a diagonal.

To find side DG, we need to use Pythagorean's Theorem, where GE is hypothenuse

$GE ^{2}=11^{2}+DG^{2}\\28^{2}-11^{2}=DG^{2}\\DG=\sqrt{784-121}=\sqrt{663}\\ DG \approx 25.75$

This figure is also a rectangle, which means all four interior angles are right, that is, equal to 90°, which means angle 11 and the 59° angle are complementary, so

$\angle 11 +59\°=90\°\\\angle 11=90\°-59\°\\\angle 11=31\°$

Now, angles 11 and 4 are alternate interior angles which are congruent, because a rectangle has opposite congruent and parallel sides.

$\angle 4 = 31\°$

Which means $\angle 3 = 59\°$ , beacuse it's the complement for angle 4.

Now, $\angle 6 = 59\°$ , because it's a base angle of a isosceles triangle. Remember that in a rectangle, diagonals are congruent, and they intersect equally, which creates isosceles triangles.

$\angle 9=180-59-59=62$ , by interior angles theorem.

$\angle 8 =62$ , by vertical angles theorem.

$\angle 10 = 180- \angle 9=180-62=118\°$ , by supplementary angles.

$\angle 7 = 118\°$ , by vertical angles theorem.

$\angle 5=90-59=31$ , by complementary angles.

$\angle 2 = \angle 5 = 31\°$ , by alternate interior angles.

$\angle 1 = 59\°$ , by complementary angles.

$m\angle BCD=90\°$ , because it's one of the four interior angles of a rectangle, which by deifnition are equal to 90°.

$m\angle ABD = 6\° = m\angle BDC$ , by alternate interior angles and by given. $m\angle CBE=90-6=84$ , by complementary angles.

$m\angle ADE=90-6=84$ , by complementary angles.

$m\angle AEB=180-6-6=168\°$ , by interior angles theorem.

$m\angle DEA=180-168=12$ , by supplementary angles.

$m\angle JMK=180-126=54$ , by supplementary angles.

$m\angle JKH=\frac{180-54}{2}=\frac{126}{2}=63$ , by interior angles theorem, and by isosceles triangle theorem.

$m\angle HLK=90\°$ , by definition of rectangle.

$m\angle HJL=\frac{180-126}{2}=27$ , by interior angles theorem, and by isosceles triangle theorem.

$m\angle LHK=90-27=63$ , by complementary angles.

$m\angle = JLK= m\angle HJL=27$ , by alternate interior angles.

The figure is a rectangle, which means its opposite sides are equal, so

$WZ=XY\\7x-6=3x+14\\7x-3x=14+6\\4x=20\\x=\frac{20}{4}\\ x=5$

Then, we replace this value in the expression of side WZ

$WZ=7x-6=7(5)-6=35-6=29$

Therefore, side WZ is 29 units long.

We know that the diagonals of a rectangle are congruent, so

$SQ=PR\\11x-26=5x+28\\11x-5x=28+26\\6x=54\\x=\frac{54}{6}\\ x=9$

Then,

$PR=5x+28=5(9)+28=45+28=73$

Therefore, side PR is 73 units long.

3 0

2 years ago

Paul bought a package of 6 spiral notebooks for a total cost of $13.50. which equation represents p, the cost, in dollars, of ea

jek_recluse [69]

6p=13.50

there are 6 notebooks and it costs $13.50 altogether. P represents the cost of one notebook, therefore the equation would be 6p=13.5. It can be rearranged to p=13.5/6

5 0

2 years ago

You have been hired as a marketing consultant to Johannesburg Burger Supply, Inc., and you wish to come up with a unit price for

kotegsom [21]

Answer:

q(p)= -3000p+12000

Step-by-step explanation:

For the function to be linear,

q(p)= mp + c

where

q(p): number of hamburgers sold

p: price per hamburger

m: gradient of the function

c: constant of the function

q(p)=6000 when p=2

6000=2m+c .................... equation I

0=4m+c

c=-4m........................ equation II

Substitute value of c in equation I

6000=2m-4m

m= -3000

c=12000

q(p)= -3000p+12000

6 0

2 years ago

The graph shows that Chelsea can type 175 words in minutes.

ivolga24 [154]

Good for chelsa. Whats the question here lol. comment it so I can help

5 0

2 years ago