substitution

Sam has $2.25 in quarters and dimes, and the total number of coins is 12. How many quarters and how many dimes? Let d be the number of dimes. Let q be the number of quarters. We're given two equations: 0.1d + 0.25q = 2.25 d + q = 12 We have a simultaneous system of equations. We can solve...

George has a certain number of apples, and Sarah has 4 times as many apples as George. They have a total of 25 apples. Let George's apples be g. Let Sarah's apples be s. We're give two equations: s = 4g g + s = 25 Substitute equation (1) into equation (2) for s: g + 4g = 25 If we plug this...

Ahmad has a jar containing only 5-cent and 20-cent coins. In total there are 31 coins with a total value of $3.50. How many of each type of coin does Ahmad have? Let the number of 5-cent coins be f. Let the number of 20-cent coins be t. We're given two equations: f + t = 31 0.05f + 0.2t =...

A first number plus twice a second number is 22. Twice the first number plus the second totals 28. Find the numbers. Let the first number be x. Let the second number be y. We're given two equations: x + 2y = 22 <-- Since twice means multiply by 2 2x + y = 28 <-- Since twice means multiply by...

On the first day of ticket sales the school sold 3 senior citizen tickets and 10 child tickets for a total of $82. The school took in $67 on the second day by selling 8 senior citizen tickets And 5 child tickets. What is the price of each ticket? Let the number of child tickets be c Let the...

A movie theater charges $7 for adults and $3 for seniors on a particular day when 324 people paid an admission the total receipts were 1228 how many were seniors and how many were adults? Let the number of adult tickets be a. Let the number of senior tickets be s. We're given two equations: a...

a football team won 3 more games than it lost.the team played 11 games.how many did it win? Let wins be w. Let losses be l. We're given two equations: w = l + 3 l + w = 11 Plug equation (1) into equation (2) to solve for l: l + (l + 3) = 11 Group like terms: 2l + 3 = 11 Typing this equation...

A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add their ages is equal 100 Let the man's age be m. Let the wife's age be w. Let the daughter's age be d. We're given: m = w + 5 d = 0.5m d + m + w = 100 Rearrange equation 1 in terms of w my...

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test? Let the number of true/false questions be t. Let the number of multiple choice...

Jill and Jack are getting vegetables from the Farmer's Market. Jill buys 12 carrots and 8 tomatoes for $34. Jack buys 10 carrots and 7 tomatoes for $29. How much does each carrot and each tomato cost? Let the cost of carrots be c and the cost of tomatoes be t. Since the total cost is price...

At a carnival, the price of an adult ticket is $6 while a child ticket is $4. On a certain day, 30 more child tickets than adult tickets were sold. If a total of $6360 was collected from the total ticket sale that day, how many child tickets were sold? Let the number of adult tickets be a. Let...

Jack has 34 bills and coins in 5’s and 2’s. The total value is $116. How many 5 dollar bills does he have? Let the number of 5 dollar bills be f. Let the number of 2 dollar bills be t. We're given two equations: f + t = 34 5f + 2t = 116 We have a system of equations, which we can solve 3...

A first number plus twice a second number is 3. Twice the first number plus the second totals 24. Let the first number be x. Let the second number be y. We're given: x + 2y = 3 <-- Because twice means multiply by 2 2x + y = 24 <-- Because twice means multiply by 2 We have a system of...

Tyrone re sells 3 pairs of Yeezys and a pair of Nikes for 250$. Nucci re sells a pair of Yeezys and Nikes for 150$ How much does a pair of Yeezys cost? Let y be the cost of Yeezy's and n be the cost of Nike's. We're given two equations: 3y + n = 250 y + n = 150 We have a system of equations...

Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he is able to buy 5 packages of paper and 6 staplers for $62. How much does a package of paper cost? How much does a stapler cost? Let the cost of paper packages be p and the cost of staplers be s...

A movie theater charges 7.00 for adults and 2.00 for seniors citizens. On a day when 304 people paid for admission, the total receipt were 1118. How many who paid were adults ? How many were senior citizens? Let a be the number of adult tickets. Let s be the number of senior citizen tickets...

Kevin and Randy Muise have a jar containing 52 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $6.20. How many of each type of coin do they have? Let q be the number of quarters, and n be the number of nickels. We have: n + q = 52 0.05n + 0.25q =...

Does the point (2, 4) satisfy the equation y = 2x? Plug in x = 2 to y = 2x: y = 2(2) y = 4 Yes, the point (2,4) satisfies the equation y = 2x

Half of a pepperoni pizza plus 3/4ths of a ham and pineapple pizza has 765 calories. 1/4th of a pepperoni pizza and a whole ham and pineapple pizza contains 745 calories. How many calories are each of the 2 kinds of pizzas individually? Let p be the pepperoni pizza calories and h be the ham and...

Rachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On Wednesday, she sold 6 fewer books than she did on Tuesday. During the 3 days Rachel sold 19 books. Create an equation that can be used to find m, a number of books Rachel sold on Monday. Let me be the...