Answer:
(2, 1)
Step-by-step explanation:
The best way to do this to avoid tedious fractions is to use the addition method (sometimes called the elimination method). We will work to eliminate one of the variables. Since the y values are smaller, let's work to get rid of those. That means we have to have a positive and a negative of the same number so they cancel each other out. We have a 2y and a 3y. The LCM of those numbers is 6, so we will multiply the first equation by a 3 and the second one by a 2. BUT they have to cancel out, so one of those multipliers will have to be negative. I made the 2 negative. Multiplying in the 3 and the -2:
3(-9x + 2y = -16)--> -27x + 6y = -48
-2(19x + 3y = 41)--> -38x - 6y = -82
Now you can see that the 6y and the -6y cancel each other out, leaving us to do the addition of what's left:
-65x = -130 so
x = 2
Now we will go back to either one of the original equations and sub in a 2 for x to solve for y:
19(2) + 3y = 41 so
38 + 3y = 41 and
3y = 3. Therefore,
y = 1
The solution set then is (2, 1)
Answer:
Step-by-step explanation:
We first need to figure out how much money Jackie has since Pilar has the same amount of money, but in different coins. Jackie has 24 dimes and 13 quarters, so the amount of money is $2.40 + $3.25 = $5.65; therefore, Pilar has $5.65 also. In order to determine how many nickels and quarters Pilar has, we have to have a system of equations. It's up to us to write the equations we need to solve this. The first equation has to do with the NUMBER of coins Pilar has, the second has to do with the VALUE of each coin. We know that Pilar has only nickels and quarters and that she has a total of 53 coins. So the NUMBER equation is
n + q = 53
The VALUE equation relates how much each coin is worth to the total amount of money it equals:
.05n + .25q = 5.65.
Go back to the first equation and solve it for either n or q. I solved it for n:
n = 53 - q
Plug this into the second equation in place of n now to get:
.05(53 - q) + .25q = 5.65 and
2.65- .05q + .25q = 5.65 and
.20q = 3 so
q = 15. This means that there are 15 quarters. If there are 15 quarters, then there are
n + 15 = 53 nickels and
n = 38 nickels.
Answer:14+8c
Step-by-step explanation:
Answer:
0.8988
Step-by-step explanation:
the first digit is tenths, then hundredths, then thousandths, then tenthousanths, so you know your end result will have four digits after the decimal. since 9 is greater than 5, you round up the seven before it to an 8. the result is 0.8988
Answer:
b has 79,775 million
a has 241,275 million
Step-by-step explanation:
a has more than b
b+161,500 is a
b=b
b+b+161,500=321,050
2b=321,050-161,500
2b=159,550
b=159,550/2
b=79,775
a=b+161,500
a=79,775+161,500
a=241,275
