Math word problem help?

Question

A jar contains 76 coins consisting of dimes and quaters, worth a total of $13.90. How many dimes are in the jar?

Answer 1

d = number of dimes
q = number of quarters

10d + 25q = 1390
d + q = 76 (mult by -10)
-10d - 10q = -760

15q = 330

q = 22

d = 76 - 22 = 54 dimes

Answer 2

d=Dimes;q=Quarters
D+Q= Total Number of Coins(76)
.1D+.25Q= Total Price
Now, the way you do this is to simplify the problem, move the decimal over two places
So, (.10D+.25Q=13.90)===
10D+25Q=1390 and
D+Q=76; Now, we have to pick a variable to solve the equation above the last one, so we will use Q=76-D, if we do this, then we can find out the total number of Dimes, without having to find the Quarters first. this is logical because if we take the total number of Dimes from the total number of coins, then it is only logical that we will find the number of Quarters, which i know that isn't what you are looking for, but it will make sense later. Now, we need to substitute the new answer we got with Q, since Q=76-D
10D+25Q=1390
10D+25(76-D)=1390, now, we use the distributive property of multiplication
10D+(25*76)+(25*-D)or 10D+(25*76)-(25*D) because the D is negative, you can change it to positive if you do it the second way. so you get
10D+1900-25D=1390, now, we simplify
-15D+1900=1390
now we need to move the 1900 to the right side of the equal sign, we can do this by changing it to its opposite, so we get
-15D= 1390-1900, now, simplify the right side,
-15D=-510, now we have to divide by 15 to get the number of dimes
-15D/-15=-510/-15
D=34 Vowala, theres the number of dimes, now if you needed the quarters subtract the number you got from 76, aka, the total number of coins,
76-34=42=Q!!!!!!
thus, 34+42=76, which means it's right!!!!!!!!

Answer 3

34 dimes.
If all the coins were quarters,there would have been $19 in the jar.
But there is only $13.90 or $5.10 less in the jar.This is because there were some dimes also in the jar
Difference of value between one quarter and one dime=$0.15
Therefore no of dimes in the jar
=5.10/0,15=34

Answer 4

Let D=the number of Dimes and Q=the number of Quarters
We have two unknowns, so we will need at least 2 equations to solve it.

First:
76=D+Q there are 76 dimes and quarters
and Q = 76 -D
Next:
If we multply the number of dimes times 10 cents and the number of quarters time 25 cents, we get $13.90
13.90=(0.10)*D + (0.25)*Q

Now use the Q=76-D to replace the Q in the money calculation:
13.90=(0.10)*D + (0.25)*(76 - D)
13.90=(0.10)*D + (0.25)*(76) - (0.25)(D)
13.90=(0.10)*D - (0.25)*D + (0.25)(76) rearrange
13.90= -0.15D + 19 combine like terms and multiply numbers
-5.1 = -0.15D divide both sides by -0.15
34=D=# of dimes

Answer 5

d + q = 76
10d + 25q = 1390
q = 76-d
10d + 25(76-d) = 1390
10d + 1900 - 25d = 1390
510 = 15d
d = 34

Answer 6

d + q = 76
10d + 25q = 1390
q = 76-d
10d + 25(76-d) = 1390
10d + 1900 - 25d = 1390
510 = 15d
d = 34

Answer 7

190 Dimes

Answer 8

34 dimes and 42 quarters

Answer 9

Math gives me a diaper rash (oh no, I feel an itch come on right now!)