Assistance with algebra word problem

(Question)

Broad street divides Popperville into an east side and a west side. On the east side of Popperville, 20% of the children qualify for a reduced-priced lunch. On the west side of Poppervile, 30% of the children qualify for a reduced-price lunch. Is it correct to calculate the percentage of children in all of Popperville who qualify for a reduced-priced lunch by adding 20% and 30% to get 50%? If the answer is no, why not? Explain in detail and calculate the correct percentage in at least two examples.

Re: Assistance with algebra word problem

Green 11

Think ...does the Broad street divides the city equally.i.e 50% of the east side and 50% of the west side? as far as the population is concerned?

you don't know and I believe it doesnt..therefore how can you add the two percentages for the whole city?...

Suppose the east side has 10000 sitizens and the west has 20000 citizens then the total population of the city is 30000 and the 50% is 15000 .

now get the 30% 0f 10000 they are 3000 get the 20% of the 20000 they are 4000 add them together....what you see? 7000 even the half of the 15000

therefore NO YOU CANNOT ADD THE TWO PERCENTAGES....

MINOAS

Re: Assistance with algebra word problem

Hello, green11!

Quote:

Broad Street divides Popperville into an east side and a west side.

On the east side of Popperville, 20% of the children qualify for a reduced-priced lunch.

On the west side of Poppervile, 30% of the children qualify for a reduced-price lunch.

Is it correct to calculate the percentage of children in all of Popperville who qualify for a reduced-priced lunch

by adding 20% and 30% to get 50%? . Certainly not!

If the answer is no, why not?

Explain in detail and calculate the correct percentage in at least two examples.

Suppose the east side has 40% and the west side has 60%.

Would we say: $\displaystyle 40\% + 60\% \,=\,100\%$

. . and conclude that *all* children qualify for a RPL?

Example #1

$\displaystyle \begin{array}{ccccccc}\text{East side has 100 children. } & 20\%\times 100 \,=\,20\text{ RPL children} \\\text{West side has 100 children. } & 30\%\times100 \,=\,30\text{ RPL children}\end{array}$

$\displaystyle \text{Total percent} \:=\:\frac{50}{200} \:=\:0.25 \:=\:25\%$

Example #2

$\displaystyle \begin{array}{ccccccc}\text{East side has 200 children. } & 20\%\times 200 \,=\,40\text{ RPL children} \\\text{West side has 300 children. } & 30\%\times300 \,=\,90\text{ RPL children}\end{array}$

$\displaystyle \text{Total percent} \:=\:\frac{130}{500} \:=\:0.26 \:=\:26\%$