Mid Test grade 7 ratio, persentage and sequences

The number of $2 coins, the number of 50-cent coins, and the number of 10-cent coins in a piggy bank are in the ratio 3:2:4. If four of the $2 coins are exchanged for an equal value in 50-cent coins, the ratio of the number of $2 coins to the number of 50-cent coins becomes 1:3. Find the total value of the coins in the piggy bank.

• $20

• $20.69

• $29.60

• $26.90

A train took 5 1/4 hours to travel 420 kilometers from City A to City B. It used 40 liters of fuel for the journey.

(a) Find the train's average speed.

(b) Find the fuel consumption rate in km/liter.

(c) The train traveled at an average speed of 90 km/h on a straight track for 3 hours during its journey. Find its average speed for the remaining part of the journey.

• (a) 80km/h | (b) 10.5 km/liter | (c) 66.67 km/h

• (a) 75 km/h | (b) 11.0 km/liter | (c) 77.6 km/h

• (a) 60 km/h | (b) 16.7 km/liter | (c) 80.77 km/h

• (a) 90 km/h | (b) 18.2 km/liter | (c) 77.67 km/h

For a performance at the Sydney Opera House in 2024, the price of a Premium ticket to that of a Standard ticket is 7:3, and the price of a Standard ticket to that of a Budget ticket is 5:2.

a. Find the ratio of the price of a Premium ticket to that of a Standard ticket to that of a Budget ticket.

b. If the price of a Budget ticket is $18, find the price of a Premium ticket.

• 6:15:35

• 15:6:35

• 35:15:6

• 30:35:15

The cost of making a chair is $450, of which 60% is the material cost and the remaining is the labor cost.

(a) Find the cost of:

(i) labor,

(ii) material used.

(b) If the cost of material is increased by 10% while the cost of labor is decreased by 5%, find the percentage change in the cost of making the chair.

• (a) $270 | $180 (b) an increase of 4%

• (a) $180 | $270 (b) decrease of 4%

• (a) $270 | $180 (b) decrease of 4%

• (a) $180 | $270 (b) an increase of 4%

A tablet originally costs $800 and is given a 20% discount. After the first discount, the store applies an additional 10% discount on the new price. What is the final price of the tablet?

• $576

• $567

• $657

• $675

A baker is making a multi-tiered cake. The first tier has 12 strawberries, the second tier has 16 strawberries, the third tier has 20 strawberries, and so on, following the same pattern. How many strawberries are on the 18th tier?

• 90

• 80

• 70

• 60

For the following sequences, find its general term and next two terms.

5, 11, 17, 23, ...

• an = 6n-1 | 29,35

• an=5n-1 | 28,34

• an = 4n-1 |27, 33

• an=3n-1 |26, 32

For the following sequences, find its general term and next two terms.

81, 27, 9, 3, ...

• an = 81(⅓) ^n-1 | 1 , ⅓

• an = 85(⅓) ^n-1 | 2 , 4

• an = 81(½) ^n-1 | 1 , ½

• an = 81(⅓)^n-1 | 1 , ½

In a theater, chairs are arranged in rows. The first row has 8 chairs, the second row has 12 chairs, the third row has 16 chairs, and so on.

a. How many chairs are in the 15th row? b. Which row has 100 chairs?

• (a) 65 (b)25

• (a) 64 (b) 24

• (a) 63 (b) 23

• (a) 62 (b) 22

Consider the pattern formed by black and gray hexagon tiles in the figures bellow, where n is the figure number.

Let Tn be the number of gray tiles in the figure n.

a. How many gray tiles in figure 30 ?

b. Which figure has 600 gray tiles?

• (a) 140 (b) 100

• (a) 180 (b) 150

• (a) 180 (b) 100

• (a) 100 (b) 180