Start by setting out what we know in equations.
D = 0.10
Q = 0.25
X(0.10) + Y(0.25) = 2.25
X = 2Y
Now, replace the X in the longer equation with its known Y equivalent.
2Y(0.10) + Y(0.25) = 2.25
Multiply out the brackets
0.2Y + 0.25Y = 2.25
Add the Y values together
0.45Y = 2.25
Divide both sides by 0.45
Y = 5
So, now we can replace the Y in the longer equation
X(0.10) + 5(0.25) = 2.25
and resolve that
X(0.10) + 1.25 = 2.25
X(0.10) = 2.25 - 1.25
X(0.10) = 1.00
X = 10
So, there are ten dimes and five quarters.
7
He has 165 cents.
6 pennies
117 Alternative method: If all the coins were dimes he would have $41.90; He is $5.85 short of that figure Every 5c short represents 1 nickel replacing a dime 585/5 = 117 nickels (and 302 dimes).
You could have: 8 nickels and 1 penny or 6 nickels and 11 pennies or 4 nickels and 21 pennies or 2 nickels and 31 pennies. The option of 0 nickels and 41 pennies is excluded by the necessity that the amount is made up of dimes, nickels and pennies; 0 nickels would mean the $1.21 was made up of dimes and pennies only.
Start by setting out what we know in equations. D = 0.10 Q = 0.25 X(0.10) + Y(0.25) = 2.25 X = 2Y Now, replace the X in the longer equation with its known Y equivalent. 2Y(0.10) + Y(0.25) = 2.25 Multiply out the brackets 0.2Y + 0.25Y = 2.25 Add the Y values together 0.45Y = 2.25 Divide both sides by 0.45 Y = 5 So, now we can replace the Y in the longer equation X(0.10) + 5(0.25) = 2.25 and resolve that X(0.10) + 1.25 = 2.25 X(0.10) = 2.25 - 1.25 X(0.10) = 1.00 X = 10 So, there are ten dimes and five quarters.
7
There is an extremely large amount of possibilities of money combinations that could be within a piggy bank. We must first note that some piggy banks differ in size, but the real problem is with the change itself. The piggy bank could be filled with all pennies, all quarters, 10 dimes and the rest quarters, and so on. The possibilities are limitless.
7
thirty-five 3 x 0.25 = 0.75 and 97 x 0.10 = 9.70 so total 10.45 [wrong] 25 x 0.25 = 6.25 and 75 x 0.10 = 7.50 so total 13.75 [wrong] 41 x 0.25 = 10.25 and 59 x 0.10 = 5.90 so total 16.15 [wrong] 65 x 0.25 = 16.25 and 35 x 0.10 = 3.50 so total 19.75 [correct] Answer: 35 dimes (and 65 quarters)
Work in cents. 10D + 25Q = 1975 and D + Q = 100 so D = 100 - Q 1000 - 10Q + 25Q = 1975 15Q = 975 Q = 65 making D = 35; Check: does 10 x 35 + 65 x 25 = 1975? 350 + 1625 = 1975. Game over.
He has 165 cents.
6 pennies
117 nickles
117 Alternative method: If all the coins were dimes he would have $41.90; He is $5.85 short of that figure Every 5c short represents 1 nickel replacing a dime 585/5 = 117 nickels (and 302 dimes).
Let X equal the number of quarters X * 25 is the value of the quarters ((X+8) * 5) is the value of the nickels25X + 5X + 40 = 610 so 30X + 40 = 610 .subtract 40 from both sides , divide both sides by 30X = 19There are 19 quarters and 27 nickels in the piggy bank
piggy