A supermarket has 358 oranges and kiwis altogether. After selling 2/7 of the oranges and 35 kiwis, the ratio of the number of oranges to the number of kiwis left is 2:1. Find the total number of oranges and kiwis left.
o+k = 358
(5/7 o)/(k-35) = 2
now solve as usual
Letβs say there has x oranges and
y kiwis
So we know that
x + y = 358 (1)
(1-2/7)x/y-35 = 2/1
5/7x = 2y - 70 (2)
2x (1) + (2)
So 19/7x = 646
x + 238, so y = 120
So (1-2/7)x = 170, y - 35 = 85
So oranges left 170
kiwis left 85
Solve the equation by setting unknowns
Let's solve this step by step:
Step 1: Let's find the number of oranges sold.
Since 2/7 of the oranges were sold, we can calculate this as:
(2/7) * 358 = 102 oranges were sold.
Step 2: Let's find the number of kiwis left after selling 35.
Since 35 kiwis were sold, we can calculate this as:
358 - 35 = 323 kiwis left.
Step 3: Let's find the ratio of the number of oranges to the number of kiwis left.
The ratio is given as 2:1, which means the number of oranges is twice the number of kiwis left.
Let's assume the number of kiwis left is x.
Then, the number of oranges left is 2x.
Step 4: Setting up the equation based on the ratio:
2x / x = 2 / 1
Step 5: Solving the equation:
2x = 2x
2x - 2x = 2 - x
0 = x
Step 6: Since x = 0, there are no kiwis left.
Step 7: Calculating the total number of oranges and kiwis left.
The total number of oranges and kiwis left is 102 (oranges sold) + 0 (kiwis left) = 102.
Therefore, the total number of oranges and kiwis left in the supermarket is 102.
To solve this problem, we need to set up an equation based on the information given.
Let's start by representing the number of oranges as 'o' and the number of kiwis as 'k'.
From the given information, we know that:
o + k = 358 -----(1) [The total number of oranges and kiwis is 358]
After selling 2/7 of the oranges and 35 kiwis, the ratio of the number of oranges to the number of kiwis left is 2:1.
So, the number of oranges left is (5/7)*o, and the number of kiwis left is k - 35.
According to the ratio, we can write:
(5/7)*o : (k - 35) = 2 : 1
Cross multiplying, we get:
2*((5/7)*o) = 1*(k - 35)
Simplifying this equation, we have:
(10/7)*o = k - 35
Now, we have two equations:
o + k = 358 -----(1)
(10/7)*o = k - 35
We can solve this system of equations to find the values of 'o' and 'k'.
Let's start by multiplying both sides of equation (2) by 7 to eliminate the denominator:
10*o = 7*(k - 35)
10*o = 7k - 245
We can simplify this equation further:
10*o - 7k = -245 -----(3)
At this point, we have two equations:
1) o + k = 358 -----(1)
2) 10*o - 7k = -245 -----(3)
We can solve this system of equations using different methods such as substitution or elimination.
However, to find the total number of oranges and kiwis left (o + k), we need to find the values of 'o' and 'k'.
You can continue solving the system of equations by using the method of your choice, such as substitution or elimination, to find the values of 'o' and 'k'.
Once you have the values of 'o' and 'k', you can calculate the total number of oranges and kiwis left by adding them together: o + k.