13. Liza is 6 years younger than her brother Nic. If the sum of their ages is 24...

Questions

October 2022 1 1 Report

13. Liza is 6 years younger than her brother Nic. If the sum of their ages is 24, how old is Liza
14. From problem number 13, how old is nic?
15. The length of a rectangle is twice its width. If its perimeter is 36, how long is its width?

Answers & Comments

KAntoineDoix

Verified answer

✏️ALGEBRA

==============================

#13: Liza is 6 years younger than her brother Nic. If the sum of their ages is 24, how old is Liza?

» Represent their ages as variables:

x = Age of Liza
y = Age of Nic

» Make equations on the given statements:

$\begin{cases} \sf x = y - 6 \\ \sf x + y = 24 \end{cases}$

» Solve for Liza's age:

$\begin{cases} \sf y = x + 6 \\ \sf x + y = 24 \end{cases}$

$\begin{cases} \sf y = x + 6 \\ \sf x + (x + 6) = 24 \end{cases}$

$\begin{cases} \sf y = x + 6 \\ \sf x + x + 6 = 24 \end{cases}$

$\begin{cases} \sf y = x + 6 \\ \sf x + x = 24 - 6 \end{cases}$

$\begin{cases} \sf y = x + 6 \\ \sf 2x = 18 \end{cases}$

$\begin{cases} \sf y = x + 6 \\ \sf \frac{\cancel2x}{\cancel2} = \frac{18}{2} \end{cases}$

$\begin{cases} \sf y = x + 6 \\ \sf x = 9 \end{cases}$

$\large \therefore \underline{\boxed{\tt \purple{Liza \: is \: 9 \: years \: old}}}$

$\:$

#14: From problem number 13, how old is Nic?

$\begin{cases} \sf y = x + 6 \\ \sf x = 9 \end{cases}$

$\begin{cases} \sf y = 9 + 6 \\ \sf x = 9 \end{cases}$

$\begin{cases} \sf y = 15 \\ \sf x = 9 \end{cases}$

$\large \therefore \underline{\boxed{\tt \purple{Nic \: is \: 15 \: years \: old}}}$

$\:$

#15: The length of a rectangle is twice its width. If its perimeter is 36, how long is its width?

» Represent the given dimensions and perimeter as variables.

P = Perimeter
l = Length
w = Width

» Make equations on the given statements.

$\begin{cases} \sf l = 2w \\ \sf P = 2l + 2w \\ \sf P = 36 \end{cases}$

» Solve for the width:

$\begin{cases} \sf l = 2w \\ \sf 36 = 2(2w) + 2w \\ \sf P = 36 \end{cases}$

$\begin{cases} \sf l = 2w \\ \sf 36 = 4w + 2w \\ \sf P = 36 \end{cases}$

$\begin{cases} \sf l = 2w \\ \sf 36 = 6w \\ \sf P = 36 \end{cases}$

$\begin{cases} \sf l = 2w \\ \sf \frac{36}{6} = \frac{\cancel6w}{\cancel6} \\ \sf P = 36 \end{cases}$

$\begin{cases} \sf l = 2w \\ \sf 6 = w \\ \sf P = 36 \end{cases}$

$\begin{cases} \sf l = 2w \\ \sf w = 6 \\ \sf P = 36 \end{cases}$

$\large \therefore \underline{\boxed{\tt \purple{The \: width \: is \: 6 \: units \: long}}}$

==============================

#CarryOnLearning

(ノ^_^)ノ

jocelyncelyntuvera ty

KAntoineDoix You're welcome (◔‿◔)

johndirkcamancho2 sorry 2 lang yung hearts^^

johndirkcamancho2 hindi gumana

UK2019 galing

Add an Answer

Questions

Answers & Comments

Verified answer

✏️ALGEBRA

==============================

==============================

Add an Answer

pa answer po75180dff711a0e832e5c489c316fdaa3 56477

texa473168d71a5859199f0d12a896c0f62 4556

pa answer po pls pasahan nanmin bukasd8f1c1ef915bf6f3ddcedb05deb83732 53471

tex1203d54d3c1e8faa4c36daf8faa93bf2 50224

tex7b99d99c2bcd62d34482980f2007388a 5382

tex2c41f5760ffb9fc7848fb18793d5b736 81195

pa answer po97247729f86586167fc45f53651d3201 20973

106ac202a2a6737ae87b18f33a5a90ce

tex1cddd9c1140c2549aec06b36691a6237 66644

pa answer po plsba5bb60921d5bf1078094309a6fc6d49 71232

Recommend Questions

Helpful Links

Helpful Social