In word problems, a system of equations appears when there are two unknown quantities and two independent relationships between them.
Algorithm:
1) introduce the unknowns,
2) write equations from the phrases in the statement,
3) solve the system,
4) state the answer in the language of the problem.
Each equation in the system should follow directly from the text
Do not start calculating before you have written the definitions
State the answer using the units and terms from the problem
A store received 450 kg of bananas. On the second day they sold 54 of the amount sold on the first day, and on the third day — 32 of the amount sold on the first day. How many kilograms were sold on the second day?
Let x be the kg sold on the first day. Then on the second day they sold 54x kg, and on the third — 32x kg.
From the condition:
x+54x+32x=450.
Multiply by 15:
15x+12x+10x=6750,
37x=6750,
x=376750.
Then on the second day:
54x=54⋅376750=375400≈145.95 kg.
First pick a convenient unknown — the amount sold on day 1
Turn the fractions of that unknown into coefficients
After finding x, answer what the problem actually asks for
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