# Algebra - math word problems

1. A candle A candle shop sells scented candles for \$16 each and unscented candles for \$10 each. The shop sells 28 candles today and makes \$400. a. Write a system of linear equations that represents the situation. b. Solve the system to answer the questions: How
2. Father 7 Father is 6 times older than his son. After 4 years, the father will only be 4 times older. What are their present ages?
3. A residential A residential colony has a population of 5400 and 60 litres of water is required per person per day. For the effective utilization of rain water, they constructed a water reservoir measuring 48m × 27m × 25m to collect the rain water. For how many days, th
4. What is What is the value of the smaller of a pair of numbers for which their sum is 78 and their division quotients are 0.3?
5. Surface of cubes Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each part made a cube. In what ratio are the surfaces of these cubes?
6. Diagonal to area Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
7. The bulbs The bulbs are connected serially two bulbs and one resistor. Each bulb has a resistivity of 100 ohms and resistor of 60 ohms The voltage source in the circuit is 24 volts. Do you know what voltage to measure on individual appliances?
8. Sixty Sixty percent of one-fifteen of the total is equal to thirty. What are two percent of the total?
9. Flying The airplane from Prague to Bratislava was flying at a speed of 60 km/h less and back by 70 km/h greater than the original speed. What was the original speed if the plane returned to Prague according to the timetable?
10. Map scale The rectangular plot has in a scale of 1: 10000 area 3 cm2 on the map. What content does this plot have on a 1:5000 scale map?
11. Girls The children's competition was attended by 63 girls, which is 30% of all children's participants. How many children attended this competition?
12. 13 tickets A short and long sightseeing tour is possible at the castle. Ticket for a short sightseeing circuit costs CZK 60, for a long touring circuit costs CZK 100. So far, 13 tickets have been sold for 1140 CZK. How much did you pay for tickets for a short tour?
13. Find the 2 Find the term independent of x in the expansion of (4x3+1/2x)8
14. A number A number increased by 7.9 is 8.3
15. Exponential warm Suppose that a body with temperature T1 is placed in surroundings with temperature T0 different from that of T1. The body will either cool or warm to temperature T(t) after time t, in minutes, where T(t)=T0 + (T1-T0)e^(-kt) . If jello salad with 30 degr
16. Perimeter of a rectangle If the perimeter of a rectangle is 114 meters and the length is twice the width plus 6 meters, what are the length and width?
17. Three points 2 The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
18. Playing How long have we trained on the pitch when we know that the warm-up took 10 minutes, we trained passes for one-third of the time and we played football half the time?
19. Curve and line The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3 (1) Find the x co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
20. Cuboid The sum of the lengths of the three edges of the cuboid that originate from one vertex is 210 cm. Edge length ratio is 7: 5: 3. Calculate the length of the edges.

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