Answer :
- Ava's height is 89 cm
- Olivia's height is 112 cm
Further explanation
Given:
- Ava is 23 cm taller than Olivia
- Olivia is half the height of Lucas
- Lucas is 1.78 m tall
Question:
How tall are Ava and Olivia?
Express their heights in centimeters.
Problem solving:
From the information above, only Lucas's tall has known at 1.78 m.
Because Olivia is half the height of Lucas, then we must multiply Lucas's height with ¹/₂ to get Olivia's tall.
[tex]\boxed{ \ Olivia's \ height = \frac{1}{2} \times 1.78 \ m \ }[/tex]
Or, we can halve Lucas's height as follows:
[tex]\boxed{ \ Olivia's \ height = 1.78 \ m \div 2 \ }[/tex]
Thus, Olivia's height is [tex]\boxed{ \ 0.89 \ meters \rightarrow 89 \ cm \ }[/tex]
Next, we find out Ava's height.
Because Ava's is 23 cm taller than Olivia’s, then we must add Olivia’s height with 23 cm to get Ava's height.
Ava's height = 89 cm + 23 cm
Thus, Ava's height is [tex]\boxed{ \ 112 \ cm \rightarrow 1.12 \ meters \ }[/tex]
We have to express their height in centimeters. Recall that 1 m = 100 cm.
Conclusion
- Ava's height is 0.89 m or 89 cm
- Olivia's height is 1.12 m or 112 cm
- Lucas's height is 1.78 m or 178 cm
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Keywords: Ava is 23 cm taller than Olivia, half the height of Lucas, 1.78 m tall, multiply, express their heights in centimeters.
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.
