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You are making backpacks for a missionary to give to school children where the missionary ministers.
Each backpack will have a children's bible, two pencils, a notebook, and an eraser.
For the youngest children, there will be a stuffed, fuzzy toy, a box of crayons and a pen.
The children in the middle group will get two pens, a ruler and an extra pencil.
The oldest group of children will the ruler, a compass, and three pens as well as the rest of the material.
There are 212 pencils, 188 pens and 92 backpacks. How many children at each age group?
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To solve the problem successfully, we need FILTER OUT all the UNNECESSAY and EXCESSIVE information.
We have data to construct equations for pencils, pens and backpacks.
THEREFORE, forget about all other irrelevant items: bibles, notebooks, erasers, toys, crayons, rulers.
Concentrate and trace only those things that DO MATTER.
Now we will construct equations.
Let x, y, and z be the number of students in the youngest, middle and oldest groups, respectively.
The equations are (write them as you read the text, and make corrections in the coefficients if needed
as you move along the text)
2x + 3y + 2z = 212 (1) (pencils)
x + 2y + 3z = 188 (2) (pens)
x + y + z = 92 (3) (backpacks)
Now the setup is completed. You have 3 equations for 3 unknowns, so the problem is solvable.
You can solve the problem by any method you want. You may even use a matrix solver of your calculator.
To save my time, I used free of charge MATRIX SOLVER from website www.reshish.com
(my favorite web-site for such purposes).
Using it, I got the answer x = 30, y = 28, z = 34.
ANSWER. 30 children in the youngest group; 28 in the middle group and 34 in the oldest group.
Solved.
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Even if somewhere I missed or incorrectly interpreted the condition, then excuse me - the text
BY DESIGN is written to confuse the reader . . .
One passage " . . . as well as the rest of the material " may confuse anyone, everybody and forever.
But I did my best, in any case . . .
And, in any case, I showed you the way on how to analyze such problems.