Answer:
Step-by-step explanation:
6/9+x=7/10
x=7/10-6/9
when adding fractions both denominators must be equal, we’ll make them 90
x=(7/10)(9/9)-(6/9)(10/10)
x=63/90-60/90
x=3/90, the greatest divisor of 3 and 90 is 3 so divide both the numerator and denominator by 3
x=(3/3)/(90/3)
x=1/30
Let's start by writing a system of linear equations:
c -> cookies
cb -> candy bars
(You can use any abbreviations to your preference)
Abby:
4 cookies
3 candy bars
$10.25 per bag
The equation would be:
4c+ 3cb = $10.25
Marissa:
2 cookies
7 candy bars
$14.75 per bag
The equation would be:
2c + 7cb = $14.75
So our linear equation system would be:
<span>4c+ 3cb = $10.25
</span><span>2c + 7cb = $14.75
I would try to get rid of one variable so I can solve for the other variable. In this case, it is easier to get rid of c since I can multiply the second equations by 2. Then it would subtract the two equations.
(2c + 7cb = $14.75) 2 = 4c + 14 cb = $29.50
4c + 3cb = $10.25
- 4c+14 cb = $29.50 (4c would get canceled.)
---------------------------------
-11 cb = - $19.25 (Divide by -11 to solve for cb)
</span> --------- -------------
-11 -11
cb = $1.75
Now we know cb (candy bar) cost, we would substitute this value into cb into one of the equations. It doesn't matter which equation you put it in. I will substitute it in the first equations.
4c + 3 (1.75) = $10.25
4c + 5.25 = $10.25 (Multiply 3 by 1.75)
-5.25 -5.25 (Subtract 5.25 on both sides)
4c = 5 (Divide by 4 on both sides to get c)
---- ---
4 4
c= 1.25
Check the work:
4(1.25) + 3(1.75)
= $10.25
2(1.25) + 7(1.75)
= $14.75
Total cost:
cookies = $1.25
candy bars = $ 1.75
Hope this helps! :)
Remark.The easiest way to do this question is to graph it. Start with that.
The red line is y = (1/3)^x
The blue line is y = 5*(1/3)^x
CommentThe red line's y intercept is (0,1)
The blue line's y intercept is (0,5)
WhyIf the x value is 0 then (1/3)^0 = 1
y = (1/3)^0 = 1 * 1 = 1 and for the blue graph
y = 5*(1/3)^0 = 5*1 = 5
In other words, in this set of equations, the 5 makes the y intercept 5 times larger than the 1 in front of y = (1/3)^x
If you have choices, could you please list them? I may be giving you the right answer but not in the form required.