(a) System of equations:
and
(b) One soda costs ![\bold{\$1.5}](https://tex.z-dn.net/?f=%5Cbold%7B%5C%241.5%7D)
(c) One taco costs ![\bold{\$2.25}](https://tex.z-dn.net/?f=%5Cbold%7B%5C%242.25%7D)
<u>SOLUTION:</u>
Given, Mrs. Galicia bought 3 tacos and 2 sodas and paid
.
The next day she went back and bought 5 tacos and 1 soda and paid
.
Let the cost of 1 tacos be m, and cost of 1 soda be n.
Now, We have to find
(a) System of equations:
3 tacos and 2 sodas cost ![\$ 9.75 \rightarrow 3 \times m+2 \times n=\$ 9.75 \rightarrow 3 m+2 n=9.75 \rightarrow(1)](https://tex.z-dn.net/?f=%5C%24%209.75%20%5Crightarrow%203%20%5Ctimes%20m%2B2%20%5Ctimes%20n%3D%5C%24%209.75%20%5Crightarrow%203%20m%2B2%20n%3D9.75%20%5Crightarrow%281%29)
5 tacos and 1 soda cost ![\$ 12.75 \rightarrow 5 \times m+1 \times n=\$ 12.75 \rightarrow 5 m+n=12.75 \rightarrow(2)](https://tex.z-dn.net/?f=%5C%24%2012.75%20%5Crightarrow%205%20%5Ctimes%20m%2B1%20%5Ctimes%20n%3D%5C%24%2012.75%20%5Crightarrow%205%20m%2Bn%3D12.75%20%5Crightarrow%282%29)
System of equations are
![5m + n = 12.75](https://tex.z-dn.net/?f=5m%20%2B%20n%20%3D%2012.75)
Now, ![(2) \rightarrow n=12.75-5 m](https://tex.z-dn.net/?f=%282%29%20%5Crightarrow%20n%3D12.75-5%20m)
So, substitute n in (1)
![\begin{array}{l}{3 m+2(12.75-5 m)=9.75} \\\\ {3 m+25.5-10 m=9.75} \\\\ {10 m-3 m=25.5-9.75} \\\\ {7 m=15.75}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B3%20m%2B2%2812.75-5%20m%29%3D9.75%7D%20%5C%5C%5C%5C%20%7B3%20m%2B25.5-10%20m%3D9.75%7D%20%5C%5C%5C%5C%20%7B10%20m-3%20m%3D25.5-9.75%7D%20%5C%5C%5C%5C%20%7B7%20m%3D15.75%7D%5Cend%7Barray%7D)
![\begin{array}{l}{m=2.25, \text { then, } n=12.75-5 \times 2.25} \\\\ {n=12.75-11.25=1.5} \\\\ {\text {SQ, } m=2.25 \text { and } n=1.5}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7Bm%3D2.25%2C%20%5Ctext%20%7B%20then%2C%20%7D%20n%3D12.75-5%20%5Ctimes%202.25%7D%20%5C%5C%5C%5C%20%7Bn%3D12.75-11.25%3D1.5%7D%20%5C%5C%5C%5C%20%7B%5Ctext%20%7BSQ%2C%20%7D%20m%3D2.25%20%5Ctext%20%7B%20and%20%7D%20n%3D1.5%7D%5Cend%7Barray%7D)
(b) cost of one soda ![\$ 1.5](https://tex.z-dn.net/?f=%5C%24%201.5)
(c) cost of one taco ![\$ 2.25](https://tex.z-dn.net/?f=%5C%24%202.25)
Mean is calculated by adding all numbers and dividing by how many there are. I have set up an equation to find x from the given mean.
![\frac{12.5 -10 -7.5 + x}{4} = 11.5](https://tex.z-dn.net/?f=%20%5Cfrac%7B12.5%20-10%20-7.5%20%2B%20x%7D%7B4%7D%20%3D%2011.5%20)
To cancel out the denominator, multiply both sides by 4.
![4(\frac{12.5 -10 -7.5 + x}{4}) = 4(11.5)](https://tex.z-dn.net/?f=%204%28%5Cfrac%7B12.5%20-10%20-7.5%20%2B%20x%7D%7B4%7D%29%20%3D%204%2811.5%29%20)
When that is done, you are left with:
![12.5 -10 -7.5 + x = 46](https://tex.z-dn.net/?f=%2012.5%20-10%20-7.5%20%2B%20x%20%3D%2046%20)
Combine like terms:
![-5 + x = 46](https://tex.z-dn.net/?f=%20-5%20%2B%20x%20%3D%2046%20)
Add 5 to both sides, cancelling out the -5 on the left.
![x = 51](https://tex.z-dn.net/?f=%20x%20%3D%2051%20)
Your answer is 51.
If you want to check your work, plug in 51 for x.
![\frac{12.5 - 10 - 7.5 + 51}{4} = 11.5](https://tex.z-dn.net/?f=%20%5Cfrac%7B12.5%20-%2010%20-%207.5%20%2B%2051%7D%7B4%7D%20%3D%2011.5%20)
![\frac{46}{4} = 11.5](https://tex.z-dn.net/?f=%20%5Cfrac%7B46%7D%7B4%7D%20%3D%2011.5%20)
You would need to use a proportion
minutes 10
people 5. 8
10 times 8 divided by 5 is 16
16 minutes it had takes to serve u8people
No not all diagonal lines are lines of symmetry! Because if you take a piece of notebook paper and fold it in half the side do not match up! hope this helps :)
Answer:
principal=1500
rate=9%=0.09
time=2
I=1500 times 0.09 times 2
I=1500 times 0.18
I=270
interest=270
total is 1500+270=1770 total paid
Step-by-step explanation: