Answer:
The larger number is -6, the smaller number is -15
Step-by-step explanation:
We have two numbers, a and b.
We know that one number is larger than another by 9.
Then we can write:
a = b + 9
then a is larger than b by 9 units.
If the greater number is increased by 10 (a + 10) and the lesser number is tripled (3*b), the sum of the two would be -41:
(a + 10) + 3*b = -41
So we got two equations:
a = b + 9
(a + 10) + 3*b = -41
This is a system of equations.
One way to solve this is first isolate one variable in one of the two equations:
But we can see that the variable "a" is already isolated in the first equation, so we have:
a = b + 9
now we can replace that in the other equation:
(a + 10) + 3*b = -41
(b + 9) + 10 + 3*b = -41
now we can solve this for b.
9 + b + 10 + 3b = -41
(9 + 10) + (3b + b) = -41
19 + 4b = -41
4b = -41 -19 = -60
b = -60/4 = -15
b = -15
then:
a = b + 9
a = -15 + 9 = -6
a = -6
4/5x + 4/3 = 2x....there are 2 ways to do this...one with fractions, one without.
with :
4/5x + 4/3 = 2x
4/3 = 2x - 4/5x
4/3 = 10/5x - 4/5x
4/3 = 6/5x
4/3 * 5/6 = x
20/18 = x
10/9 = x
without :
4/5x + 4/3 = 2x....multiply by common denominator of 15
12x + 20 = 30x
20 = 30x - 12x
20 = 18x
20/18 = x
10/9 = x
We know that Ava is paying $2 dollars per week so if L is the money that she owes and t is the number of weeks, and I is the initial debt so we can write an equation like:
Now we can replace the info we have to find the value of I so:
and we solve for I
So the final equation will be:
Dory = 11 x Carly
Together => d + c = 156
11c + c = 156
12c = 156
C = 156 : 12
C = 13
Carly biked 13 miles
Dory = 11 x c = 11 x 13 = 143 miles
Prove
143 + 13 = 156 miles together
