A pear contains 30 calories more than an apple. Ten apples have as many calories as seven pears. Find the number of calories in an apple and in a pear.
Let's assume the number of calories in an apple is 'x'.
According to the given information, a pear contains 30 calories more than an apple. So, the number of calories in a pear would be 'x + 30'.
It is also given that ten apples have as many calories as seven pears.
Therefore, we can set up the following equation:
10x = 7(x + 30)
Expanding the equation:
10x = 7x + 210
Subtracting 7x from both sides:
3x = 210
Dividing both sides by 3:
x = 70
So, the number of calories in an apple is 70 calories.
Now, substituting the value of x into the equation 'x + 30' to find the calories in a pear:
70 + 30 = 100
Therefore, the number of calories in a pear is 100 calories.
To find the number of calories in an apple and a pear, let's represent the number of calories in an apple as "A" and the number of calories in a pear as "P".
According to the given information, "A pear contains 30 calories more than an apple," so we can express this as:
P = A + 30
It is also stated that "Ten apples have as many calories as seven pears." This can be expressed as:
10A = 7P
Now, we can solve these two equations to find the values of A and P.
Substituting the value of P from the first equation into the second equation, we get:
10A = 7(A + 30)
Now we can simplify and solve for A:
10A = 7A + 210
10A - 7A = 210
3A = 210
A = 70
Substituting the value of A back into the first equation to find P:
P = 70 + 30
P = 100
Therefore, there are 70 calories in an apple and 100 calories in a pear.
x = cal in an apple
x + 30 = cal in a pear
10x = 7(x + 30)
10x = 7x + 210
3x = 210
x = 70
70 cal = apple
100 cal = pear