Math problem?
Problem:
Moya had a total of $3.10 in her pocket in only 10- and 20- cent coins. If she has 19 coins altogether, how many of each coin does she have
Favorite Answer
amount: cost total cost
a 10 10a
19-a 20 380 – 20a
10a – 20a + 380 = 310 <- sums of total costs = 3.10 dollars 70 = 10a, a=7, so b must = 12 haha i rule, i was just teaching this to my class at this tutoring place
set up the equations, according to the given:
a) x + y = 19 (total number of coins)
b) 0.10x + 0.20y = $3.10 (total money that Moya has)
to make things less confusing, multiply both sides of equation b) by 10.
new equation b): x + 2y = 31
now by using systems of equations:
x + y = 19
-(x + 2y = 31)
=> x + y = 19
-x – 2y = -31
==> -y = -12
y = 12: no. of 20-cent coins
refer to equation a) once more:
x + y = 19
x + 12 = 19
x = 7: no. of 10-cent coins
7- 10 cent coins=.70
19 coins – $3.10
can’t help you with the algebra..I’m a savant 🙂
opps, I think the blond chick has a partial starting point:
let x be the number of 20 cent coins needed
ley y be the number of 10 cent coins needed
.20x+.10y= 3.10
x+y= 19
therfore x=19-y
solve
.20(19-y)+.10y=3.10
3.8- .20y +.10y=3.10
3.8 -.10y=3.10 (somehow aznkid above got here immediately
-.10y= 3.10-3.8
-.10y= -.70
y=7
OK, so we know that y, the number of 10 cent coins needed is 7!! Voila…Now that we know this, solving the rest is simple 🙂
From our original equation:
.20x + .10y =3.10
.20x+.10(7)= 3.10
.20x +.70 =3.10
.20x= 3.10-.70
.20x=2.40
x=12
Ok, So Algebraically, we know that the number of
10 cent pieces is 7 and the number of 20 cent pieces is 12
That’s algebra. I’m not sure what kind of space alien math aznkid is using, but it seems much faster for him :_) He jumped like 6 or 7 steps!!
It just goes to show that there are lots of ways to solve the same problem!!
x = number of 10 cent coin
y = number of 20 cent coin
(1) 10x + 20y = 310
——————— : 10
x + 2y = 31
(2) x + y = 19
x = 19 – y
substitute x in (1) with (2) so:
(19 – y) + 2y = 31
19 + y = 31
y = 12
x = 19 – 12 = 7
x + y= 19
Do the substitution method on the second equation and you get:
x = 19 – y
Now substitute it in the first equation.
.10(19 – y) + .20y = 3.10
Now solve this equation.
1.90 – .10y + .20y = 3.10 Distributive Property
-.10y + .20y = 1.20 Subtract 1.90 to both sides.
.10y = 1.20 Add left side
y = 12
Enter in Second equation:
12 + x = 19
x = 7
So your answers are:
12 twenty cent coins, and 7 ten cent coins
7 – .10
*=multiply
