Answer :
First, we must find the height of olivia.
1m = 100cm (given, metric system)
178/2 = 89cm (olivia is 89cm tall)
Ava is 23cm taller than Olivia, so 89 + 23 would be our next step.
89 + 23 = 112cm tall
Olivia: 89cm
Ava: 112cm
1m = 100cm (given, metric system)
178/2 = 89cm (olivia is 89cm tall)
Ava is 23cm taller than Olivia, so 89 + 23 would be our next step.
89 + 23 = 112cm tall
Olivia: 89cm
Ava: 112cm
Thus, the height of ava and olivia is [tex]\boxed{112\text{ cm}\text{ and }89\text{ cm}}[/tex] respectively.
Further explanation:
It is given that height of ava is [tex]23\text{ centimeter}[/tex] more than the height than the height of olivia and the height of olivia is half of the height of lucas.
Consider the height of ava, olivia and lucas as [tex]x,y[/tex] and [tex]z[/tex].
The height of the lucas is given as [tex]1.78\text{ meter}[/tex].
This implies that the value of [tex]z[/tex] is as follows:
[tex]\boxed{z=1.78}[/tex]
Since, the height of lucas is given in meter so, it is necessary to convert the unit into centimeter.
The height of lucas is converted into centimeter unit as follows:
[tex]\begin{aligned}1\text{ meter}&\rightarrow 100\text{ centimeter}\\1.78\text{ meter}&\rightarrow 1.78\times100=178\text{ centimeter}\end{aligned}[/tex]
Since, the height of olivia is half of the height of lucas so, the equation formed is as follows:
[tex]\boxed{y=\dfrac{z}{2}}[/tex]
Substitute [tex]178[/tex] for the [tex]z[/tex] in the above equation.
[tex]\begin{aligned}y&=\dfrac{178}{2}\\&=89\end{aligned}[/tex]
Therefore, the value of [tex]y[/tex] is [tex]89[/tex].
This implies that the height of olivia is [tex]89\text{ centimeter}[/tex].
It is given that height of ava is [tex]23\text{ centimeter}[/tex] more than the height than the height of olivia so, the equation formed is as follows:
[tex]\boxed{x=23+y}[/tex]
Substitute [tex]89[/tex] for [tex]y[/tex] in the above equation.
[tex]\begin{aligned}x&=23+89\\&=112\end{aligned}[/tex]
This implies that the height of ava is [tex]112\text{ centimeters}[/tex].
Thus, the height of ava and olivia is [tex]\boxed{112\text{ cm}\text{ and }89\text{ cm}}[/tex] respectively.
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Answer details:
Grade: Middle school
Subject: Mathematics
Topic: Problems on Ages
Keywords: Age, height, ava, olivia, lucas, tall, meter, centimeter, unit, conversion, 1.78, value, half of height, taller than olivia, ava is 23 cm.
