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jarptica [38.1K]
3 years ago
9

Maggie's brother is 6 years younger than four times her age. The sum of their ages is 69.

Mathematics
2 answers:
Tomtit [17]3 years ago
6 0

Answer:

15

Step-by-step explanation:

If Maggies age is, for example, x, we can say that her brothers age is 4x-6. We know from the problem that Maggies age (x) plus her bothers age, (4x-6) is 69. So,

4x-6+x=69

5x-6=69

5x=75

x=15

So, Maggie is 15.

Airida [17]3 years ago
5 0

Answer: Maggie is 15 years old

Step-by-step explanation:

69 = (4m - 6) + m     --- get an equation

69 - m = 4m - 6        --- lets subtract  m from both sides first

75 - m = 4m              --- add 6 on both sides

75 = 5m                    --- add m on both sides

15 = m                       --- divide by 5 on both sides

m = 15, so Maggie is 15 years old

Let's check:

69 = (4(15)-6) +15

69 = (60 - 6) + 15

69 = 54 + 15

69 = 69

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Which statement about the figure MUST be true? Select all that apply.
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<h2>○=> <u>Correct options</u> :</h2><h2>□\color{plum}\tt\bold{(C) \: SR = 27}</h2><h2>□\color{plum}\tt\bold{(D) \: QR = 54 }</h2><h3><u>Steps to derive the correct options</u> :</h3>

Since two sides and one included angle is equal in △PQS and △PRS, we can conclude that they are congruent under the SAS congruence criterion.

Which means :

▪︎Angle S = Angle S

▪︎PS = PS

▪︎QS = RS

Given :

Measure of segment QS = 6n+3

Measure of segment RS = 4n+11

Thus :

= \tt6n + 3 = 4n + 11

= \tt6n + 3 - 4n = 11

=\tt 2n + 3 = 11

= \tt2n = 11 - 3

= \tt2n = 8

=\tt n =  \frac{8}{2}

\hookrightarrow\color{plum}\tt n = 4

Thus, the value of n = 4

Measure of segment QS :

=\tt 6n + 3

= \tt6 \times 4 + 3

= \tt24 + 3

\color{plum}\tt \: \bold{QS = 6n + 3 = \tt\bold{27}}

Thus, measure of QS = 27

Measure of RS :

=\tt 4n + 11

=\tt 4 × 4 + 11

=\tt 16+11

\color{plum}\tt \: \bold{RS = 4n + 11 = \tt\bold{27}}

Measure of QR :

=\tt 27+27

\color{plum}\tt \: \bold{QR = 27+27 \tt\bold{=54}}

Thus :

▪︎QS = 27

▪︎RS = 27

▪︎QR = 54

Therefore, the correct options are :

▪︎(C) SR = 27

▪︎(D) QR = 54

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