You have to first make like terms
![-\frac{2}{7} -(- \frac{4}{3})- \frac{1}{3} ](https://tex.z-dn.net/?f=%20-%5Cfrac%7B2%7D%7B7%7D%20-%28-%20%20%5Cfrac%7B4%7D%7B3%7D%29-%20%20%5Cfrac%7B1%7D%7B3%7D%20%0A%20%20)
**you want the denominator to be 21
Answer:
30 fruits
Step-by-step explanation:
Let
x ----> number of plums on the plate
y ----> number of apples on the plate
we know that
The ratio of the number of plums to the number of apples was 3:2
so
![\frac{x}{y} =\frac{3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7By%7D%20%3D%5Cfrac%7B3%7D%7B2%7D)
----> equation A
After Ed took 6 plums from the plate, the number of plums remaining on the plate became the same as the number of apples
so
----> equation B
substitute equation A in equation B
![1.5y-6=y](https://tex.z-dn.net/?f=1.5y-6%3Dy)
solve for y
![1.5y-y=6\\0.5y=6\\y=12](https://tex.z-dn.net/?f=1.5y-y%3D6%5C%5C0.5y%3D6%5C%5Cy%3D12)
Find the value of x
![x=1.5(12)=18](https://tex.z-dn.net/?f=x%3D1.5%2812%29%3D18)
therefore
Mon put on the table
![x+y=18+12=30\ fruits](https://tex.z-dn.net/?f=x%2By%3D18%2B12%3D30%5C%20fruits)
300,000 dollars
20-5= 15
15 × 20,000 = 300,000
Answer:
![\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7D1%20%26%200%20%26%200%26%2046%2F41%20%26180%2F41%5C%5C0%20%26%201%20%26%200%261%2F41%20%26-5%2F41%5C%5C0%260%20%26%201%20%26%20-8%2F41%26%20-42%2F41%5Cend%7BVmatrix%7D)
Step-by-step explanation:
From the question we are told that
System of equations given as
x₁ + 3x₂ + x₃ + x₄ = 3;
2x₁ - 2x₂ + x₃ + 2x₄ = 8;
x₁ - 5x₂ + x₄ = 5
Matrix form
![\begin{Vmatrix}x_1\\x_2\\x_3\\x_4\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7Dx_1%5C%5Cx_2%5C%5Cx_3%5C%5Cx_4%5Cend%7BVmatrix%7D)
Generally the echelon reduction is mathematically applied as
![\begin{Vmatrix}1 & 3 & 1&1&3\\2 & -2 & 1&2&8\\0&1 & -5 & 1& 5\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7D1%20%26%203%20%26%201%261%263%5C%5C2%20%26%20-2%20%26%201%262%268%5C%5C0%261%20%26%20-5%20%26%201%26%205%5Cend%7BVmatrix%7D)
Add -2 times the 1st row to the 2nd row
![\begin{Vmatrix}1 & 3 & 1&1&3\\0 & -8 & -1&0&2\\0&1 & -5 & 1& 5\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7D1%20%26%203%20%26%201%261%263%5C%5C0%20%26%20-8%20%26%20-1%260%262%5C%5C0%261%20%26%20-5%20%26%201%26%205%5Cend%7BVmatrix%7D)
Multiply the 2nd row by -1/8
![\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&1 & -5 & 1& 5\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7D1%20%26%203%20%26%201%261%263%5C%5C0%20%26%201%20%26%201%2F8%260%26-1%2F4%5C%5C0%261%20%26%20-5%20%26%201%26%205%5Cend%7BVmatrix%7D)
Add -1 times the 2nd row to the 3rd row
![\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & -41/8 & 1& 21/4\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7D1%20%26%203%20%26%201%261%263%5C%5C0%20%26%201%20%26%201%2F8%260%26-1%2F4%5C%5C0%260%20%26%20-41%2F8%20%26%201%26%2021%2F4%5Cend%7BVmatrix%7D)
Multiply the 3rd row by -8/41
![\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7D1%20%26%203%20%26%201%261%263%5C%5C0%20%26%201%20%26%201%2F8%260%26-1%2F4%5C%5C0%260%20%26%201%20%26%20-8%2F41%26%20-42%2F41%5Cend%7BVmatrix%7D)
Add -1/8 times the 3rd row to the 2nd row
Add -1 times the 3rd row to the 1st row
![\begin{Vmatrix}1 & 3 & 0&49/41&165/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7D1%20%26%203%20%26%200%2649%2F41%26165%2F41%5C%5C0%20%26%201%20%26%200%261%2F41%20%26-5%2F41%5C%5C0%260%20%26%201%20%26%20-8%2F41%26%20-42%2F41%5Cend%7BVmatrix%7D)
Add -3 times the 2nd row to the 1st row
![\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7D1%20%26%200%20%26%200%26%2046%2F41%20%26180%2F41%5C%5C0%20%26%201%20%26%200%261%2F41%20%26-5%2F41%5C%5C0%260%20%26%201%20%26%20-8%2F41%26%20-42%2F41%5Cend%7BVmatrix%7D)
Answer:
Number of full size cars = 900
Step-by-step explanation:
The ratio of medium size cars to compacts is 7 to 5 and the ratio of compacts to full-size cars is 8 to 9. Since compact cars are there in both ratios , we need to make the number in the ratio for compact cars to be the same.
![\frac{medium}{compact} = \frac{7}{5}](https://tex.z-dn.net/?f=%5Cfrac%7Bmedium%7D%7Bcompact%7D%20%3D%20%5Cfrac%7B7%7D%7B5%7D)
Multiply by 8 on numerator and denominator
![\frac{medium}{compact} = \frac{56}{40}](https://tex.z-dn.net/?f=%5Cfrac%7Bmedium%7D%7Bcompact%7D%20%3D%20%5Cfrac%7B56%7D%7B40%7D)
![\frac{compact}{full size} = \frac{8}{9}](https://tex.z-dn.net/?f=%5Cfrac%7Bcompact%7D%7Bfull%20size%7D%20%3D%20%5Cfrac%7B8%7D%7B9%7D)
Multiply numerator and denominator by 5.
![\frac{compact}{full size} = \frac{40}{45}](https://tex.z-dn.net/?f=%5Cfrac%7Bcompact%7D%7Bfull%20size%7D%20%3D%20%5Cfrac%7B40%7D%7B45%7D)
Ratio of medium, compact and full size are in ratio 56,40,45.
Total number of cars =2820.
(56 + 40 + 45)x = 2820
x = ![\frac{2820}{141}](https://tex.z-dn.net/?f=%5Cfrac%7B2820%7D%7B141%7D)
x = 20
Number of full size cars =
=900