Question: Find the number of calories in an apple and a pear. A pear contains 30 calories more than an apple. Ten apples have as many calories as 7 pears.
To find the number of calories in an apple and a pear, let’s set up a system of equations based on the given information:
Let A be the number of calories in an apple.
Let P be the number of calories in a pear.
We know that:
- A pear contains 30 calories more than an apple: P = A + 30
- Ten apples have as many calories as 7 pears: 10A = 7P
We can solve these equations to find the values of A and P.
Step 1: Substitute P = A + 30 into 10A = 7P
10A = 7(A + 30)
10A = 7A + 210
10A – 7A = 210
3A = 210
A = 70
Step 2: Substitute A = 70 into P = A + 30
P = 70 + 30
P = 100
So, an apple contains 70 calories and a pear contains 100 calories.
Question: Find the number of full 8-hour shifts that Maria worked last month. She worked twice as many 6-hour shifts as 8-hour shifts. She worked a total of 280 hours.
Explanation:
We’re trying to find the number of full 8-hour shifts Maria worked. Let’s denote this number as x.
Maria also worked twice as many 6-hour shifts as 8-hour shifts, which means she worked 2x six-hour shifts.
She worked a total of 280 hours. These hours come from both the 8-hour shifts (8x hours) and the 6-hour shifts (6 * 2x = 12x hours).
Therefore, the equation to represent this situation is 8x (from the eight-hour shifts) + 12x (from the six-hour shifts) = 280.
Solution:
8x + 12x = 280
20x = 280
x = 14
Maria worked 14 full 8-hour shifts last month.
Question: Brian earns twice as much each week as a tutor than he does pumping gas. His total weekly wages are 150 more than that of his sister. She earns one quarter as much as Brian does as a tutor. How much does Brian earn as a tutor?
Explanation:
We’re trying to find out how much Brian earns as a tutor each week, and we’ll use the variable ‘T’ to represent this unknown amount.
Brian has two jobs: one as a tutor and another pumping gas. He earns ‘T’ dollars per week as a tutor and ‘T/2’ dollars per week pumping gas.
The total weekly earnings from both jobs can be summed up as ‘T + T/2’.
Brian’s sister earns ‘T/4’ dollars each week because she earns one-quarter of what Brian earns as a tutor. Brian’s total earnings are 150 dollars more than his sister’s, giving us the equation ‘T + T/2 = T/4 + 150’.
Solution:
To solve the equation ‘T + T/2 = T/4 + 150’, first multiply every term by 4 to get rid of the fractions:
4T + 2T = T + 600
Combine like terms:
6T = T + 600
Move all the terms involving ‘T’ to one side of the equation:
6T – T = 600
Simplify and solve for ‘T’:
5T = 600
T = 120
Answer: Brian earns 120 dollars per week as a tutor.