Proportional Equations Worksheets Grade 7

1. A science museum is creating a scale model of the solar system where 1 centimeter represents 12,000 kilometers. If the actual distance from Earth to Mars is approximately 78 million kilometers, what should be the distance between Earth and Mars in the scale model, measured in centimeters?
2. A construction company is building a scale model of a new bridge. The actual bridge will be 420 meters long, and the scale model uses a ratio of 1:35. If the model bridge is 12 meters long, how many centimeters wide should the model bridge be if the actual bridge is 28 meters wide?
3. Aisha is planning a road trip and uses a map app that shows the distance between cities. The app indicates that 3.5 centimeters on the map represents 210 kilometers in real life. If the distance between two cities measures 8.2 centimeters on the map, what is the actual distance between them in kilometers?

…and 5 more problems

1. Liam is mixing paint for an art project. He needs to create a specific shade of purple by mixing red and blue paint in a 3:5 ratio. If Liam uses 2.4 liters of blue paint, how many liters of red paint should he use to maintain the correct proportion?
2. Kai is filling a swimming pool with a hose. The pool gains 12 gallons of water every minute. If the pool already has 0 gallons at the start, write an equation showing the relationship between the total gallons of water, y, and the number of minutes, x. After 19 minutes, how many gallons of water are in the pool?
3. Mere earns money at a constant rate. She earns $168 for working 14 hours. Write the equation y = kx that represents her total earnings y for x hours worked.

…and 5 more problems

1. Olivia is designing a rectangular mural on a coordinate grid. The mural's corners are at (0, 0), (35, 0), (35, 20), and (0, 20). She draws a straight diagonal line from (0, 0) to (35, 20), dividing the mural into two triangular sections. The amount of red paint needed for the larger triangle is proportional to its area. If 15 square units of area require 6 liters of paint, write an equation in the form y = kx that represents the relationship between the area of the larger triangle (x) and the liters of red paint needed (y).
2. Aroha is drawing a design for a rectangular mural on a coordinate grid. The mural's corners are at (1, 3), (43, 3), (43, 19), and (1, 19). She plans to place a square photo in the center of the mural with a side length equal to one-fifth of the mural's shorter side length. The photo is placed so its sides are parallel to the mural's sides, and its center coincides with the mural's center. The remaining area of the mural will be painted with a proportional pattern where the amount of blue paint used (y, in milliliters) is proportional to the area painted (x, in square units). If 117 milliliters of blue paint are needed for every 9 square units of area, write an equation that represents the proportional relationship between the blue paint needed (y) and the area painted (x).
3. Mere is designing a mosaic on a coordinate grid. The mosaic is in the shape of a rectangle with vertices at (0, 0), (24, 0), (24, 18), and (0, 18). She wants to place a triangular pattern inside the mosaic with vertices at (0, 0), (24, 0), and (12, 18). The area of the triangular pattern is proportional to the area of the entire rectangular mosaic. Write an equation in the form y = kx that represents the proportional relationship where y is the area of the triangular pattern and x is the area of the rectangular mosaic. Then find the value of k as a simplified fraction.

…and 2 more problems