Equation From a Situation
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ISEE Lower Level: Mathematics Achievement › Equation From a Situation
Jamal is buying apples and bananas. Apples cost $0.75 each and bananas cost $0.50 each. He buys a apples and b bananas and spends exactly $10. Which equation represents this situation?
\(0.75a + 0.50b = 10\)
\(0.50a + 0.75b = 10\)
\(a + b = 10\)
\(75a + 50b = 10\)
Explanation
The total cost of the apples is the price per apple ($0.75) times the number of apples (a), which is \(0.75a\). The total cost of the bananas is the price per banana ($0.50) times the number of bananas (b), which is \(0.50b\). The sum of these costs is equal to the total amount spent, $10. So, the equation is \(0.75a + 0.50b = 10\).
In a collection of marbles, the number of red marbles, r, is exactly double the number of blue marbles, b. Which equation correctly shows this relationship?
\(b = 2r\)
\(b = r - 2\)
\(r = b + 2\)
\(r = 2b\)
Explanation
The statement 'the number of red marbles, r, is exactly double the number of blue marbles, b' means you must multiply the number of blue marbles by 2 to get the number of red marbles. This translates to the equation \(r = 2b\).
Maya is reading a book that is 350 pages long. She reads 25 pages each day. Let p be the number of pages she has left to read after d days. Which equation represents the number of pages left?
\(p = 25d\)
\(d = 350 - 25p\)
\(p = 350d - 25\)
\(p = 350 - 25d\)
Explanation
The total number of pages is 350. The number of pages read after d days is \(25d\). The number of pages left, p, is the total number of pages minus the number of pages read. This gives the equation \(p = 350 - 25d\).
The temperature in degrees Fahrenheit, F, can be found by multiplying the temperature in degrees Celsius, C, by 9, dividing the result by 5, and then adding 32. Which equation correctly represents this conversion?
\(F = \frac{9}{5}C + 32\)
\(F = 9(\frac{C}{5} + 32)\)
\(C = \frac{9}{5}F + 32\)
\(F = \frac{9}{5}(C + 32)\)
Explanation
Following the steps in order: 'multiplying the temperature in degrees Celsius, C, by 9' gives \(9C\). 'dividing the result by 5' gives \(\frac{9C}{5}\). 'then adding 32' gives \(\frac{9C}{5} + 32\). This is the value of F. The expression \(\frac{9C}{5}\) is the same as \(\frac{9}{5}C\), so the equation is \(F = \frac{9}{5}C + 32\).
Maria had $50 in her savings account. Each week, she added exactly $15. If w represents the number of weeks and A represents the total amount in her account, which equation shows the total amount after w weeks?
\(A = 50 + 15w\)
\(A = 50 - 15w\)
\(A = 15 + 50w\)
\(w = 50 + 15A\)
Explanation
The total amount A starts at $50 and increases over time. The amount added is $15 per week, which is \(15w\). Therefore, the total amount is the starting amount plus the added amount: \(A = 50 + 15w\).
A soccer team buys one jersey and one pair of shorts for each of its p players. Jerseys cost $20 each and shorts cost $15 each. Let C be the total cost for all the players' uniforms. Which equation finds the total cost?
\(C = 20p + 15\)
\(C = (20 + 15)p\)
\(C = p + 20 + 15\)
\(C = 20 + 15p\)
Explanation
First, find the cost for one player. One player needs one jersey ($20) and one pair of shorts ($15), for a total of \($20 + $15 = $35\). To find the total cost C for p players, multiply the cost per player by the number of players. This gives the equation \(C = 35p\), which is the same as \(C = (20 + 15)p\).
A movie theater sold adult tickets for $11 each and child tickets for $8 each. The total money collected was $950. If a is the number of adult tickets and c is the number of child tickets, which equation represents the total money collected?
\(11a + 8c = 950\)
\(19(a + c) = 950\)
\(a + c = 950\)
\(8a + 11c = 950\)
Explanation
The total money from adult tickets is the price per ticket ($11) times the number of tickets (a), which is \(11a\). The total money from child tickets is the price per ticket ($8) times the number of tickets (c), which is \(8c\). The total money collected is the sum of these two amounts, so \(11a + 8c = 950\).
A cell phone plan costs $25 per month, which includes 500 text messages. For each text message over 500, there is a charge of $0.10. If a person sends t text messages in a month (t is greater than 500), which equation represents the total monthly cost, C?
\(C = 25 + 0.10(500 - t)\)
\(C = 25 + 0.10t\)
\(C = 25 + 0.10(t - 500)\)
\(C = 25.10(t - 500)\)
Explanation
The base cost is $25. The extra charge only applies to texts over 500. The number of texts that are charged extra is \(t - 500\). The cost for these extra texts is \(0.10(t - 500)\). The total cost C is the base cost plus the extra charge: \(C = 25 + 0.10(t - 500)\).
A baker starts the day with a 50-pound bag of flour. He uses 3 pounds of flour for each cake, c, that he bakes. If F represents the amount of flour remaining in the bag, which equation shows the amount of flour left?
\(c = 50 - 3F\)
\(F = 50 - 3c\)
\(F = 50 + 3c\)
\(F = 3c - 50\)
Explanation
The initial amount of flour is 50 pounds. The amount used is 3 pounds per cake, so for c cakes, the amount used is \(3c\). The remaining flour, F, is the starting amount minus the amount used. This gives the equation \(F = 50 - 3c\).
A pizza is cut into 12 equal slices. After a group of friends eats s slices, what fraction, F, of the whole pizza remains?
\(F = \frac{s}{12}\)
\(F = \frac{12 - s}{12}\)
\(F = \frac{12}{s}\)
\(F = 12 - s\)
Explanation
First, find the number of slices remaining. If the pizza starts with 12 slices and s slices are eaten, there are \(12 - s\) slices left. The fraction of the pizza remaining is the number of remaining slices divided by the original total number of slices. Therefore, the fraction F is \(\frac{12 - s}{12}\).