Respuesta :
I'm not going to give you the ACTUAL answer but I'll help you out.
Read the rest of the question. There are TWO sentences. That is TWO equations. That means TWO variables. What else is involved? WRITE: Let Y = the number of xxxxx.
Rewrite each sentence as an equation (something EQUALS something) with "X" and "Y".
Remember that "less than" is a BACKWARDS subtraction: 2 less than 5 is "5-2".
For the first sentence, remember that quarters are worth $0.25, so the worth of a number of quarters is 0.25 TIMES the number of quarters. Dimes are worth $0.10, so the worth of a number of dimes is 0.10 TIMES the number of dimes. Remember that the TOTAL worth is a SUM (add to equal the total bill).
Solve one equation (either one) for Y and substitute that formula into the other equation. Solve for X. Done.
2x=4y-6 -> y=(2x+6)/4
285 = 25x+10y = 25x + 5(x+3) = 30x + 15 -> 270 = 30 x -> x=9 (y=24/4=6)
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Alternate solution - no algebra. Trial and Error:
Pick a number of quarters: Maybe 10. That makes $2.50, which leaves $0.35. That means 3.5 dimes. But twice 10 quarters is 20 and 6 less than 4 times 3.5 dimes is 8. But 20 is not equal 8, it is 12 too big.
Try a different number. Maybe 11. That makes $2.75, which leaves $0.10. That means 1 dime. But twice 11 quarters is 22 and 6 less than 4 times 1 dime is -2. But 22 is not equal -2. It is 24 too big. Worse than before!
Try again. That last guess was worse, so go in the other direction. Keep trying until you find the answer.
Read the rest of the question. There are TWO sentences. That is TWO equations. That means TWO variables. What else is involved? WRITE: Let Y = the number of xxxxx.
Rewrite each sentence as an equation (something EQUALS something) with "X" and "Y".
Remember that "less than" is a BACKWARDS subtraction: 2 less than 5 is "5-2".
For the first sentence, remember that quarters are worth $0.25, so the worth of a number of quarters is 0.25 TIMES the number of quarters. Dimes are worth $0.10, so the worth of a number of dimes is 0.10 TIMES the number of dimes. Remember that the TOTAL worth is a SUM (add to equal the total bill).
Solve one equation (either one) for Y and substitute that formula into the other equation. Solve for X. Done.
2x=4y-6 -> y=(2x+6)/4
285 = 25x+10y = 25x + 5(x+3) = 30x + 15 -> 270 = 30 x -> x=9 (y=24/4=6)
--------------
Alternate solution - no algebra. Trial and Error:
Pick a number of quarters: Maybe 10. That makes $2.50, which leaves $0.35. That means 3.5 dimes. But twice 10 quarters is 20 and 6 less than 4 times 3.5 dimes is 8. But 20 is not equal 8, it is 12 too big.
Try a different number. Maybe 11. That makes $2.75, which leaves $0.10. That means 1 dime. But twice 11 quarters is 22 and 6 less than 4 times 1 dime is -2. But 22 is not equal -2. It is 24 too big. Worse than before!
Try again. That last guess was worse, so go in the other direction. Keep trying until you find the answer.
