Understanding Fewer and More in Math

Lily has 12 fewer marbles than Tom. Tom has 8 fewer marbles than Sarah. If Lily has 10 marbles, how many marbles does Sarah have? How many marbles does Tom have? Write two equations to solve the problem.

• Sarah has 30 marbles, Tom has 22 marbles

• Sarah has 28 marbles, Tom has 20 marbles

• Sarah has 26 marbles, Tom has 18 marbles

• Sarah has 24 marbles, Tom has 16 marbles

Answer explanation

Let L = Lily's marbles, T = Tom's marbles, S = Sarah's marbles. We have L = T - 12 and T = S - 8. Given L = 10, we find T = 22 and S = 28. Thus, Sarah has 28 marbles, Tom has 20 marbles.

Emma has 7 fewer pencils than Jack. Jack has 3 fewer pencils than Mia. If Emma has 5 pencils, how many pencils does Mia have? How many pencils does Jack have? Write two equations to solve the problem.

• Mia has 15 pencils, Jack has 12 pencils

• Mia has 13 pencils, Jack has 10 pencils

• Mia has 11 pencils, Jack has 8 pencils

• Mia has 9 pencils, Jack has 6 pencils

Answer explanation

Let E, J, and M represent the number of pencils Emma, Jack, and Mia have, respectively. We know E = 5, J = E + 7, and J = M - 3. Substituting E gives J = 12 and M = 11. Thus, Mia has 11 pencils and Jack has 8 pencils.

Sam has 4 fewer apples than Ben. Ben has 6 fewer apples than Lucy. If Sam has 8 apples, how many apples does Lucy have? How many apples does Ben have? Write two equations to solve the problem.

• Lucy has 18 apples, Ben has 12 apples

• Lucy has 20 apples, Ben has 14 apples

• Lucy has 22 apples, Ben has 16 apples

• Lucy has 24 apples, Ben has 18 apples

Answer explanation

Let S = Sam's apples, B = Ben's apples, L = Lucy's apples. We have S = B - 4 and B = L - 6. Given S = 8, we find B = 12 and L = 18. Thus, Lucy has 18 apples and Ben has 12 apples.

Olivia has 9 fewer candies than Noah. Noah has 5 fewer candies than Ava. If Olivia has 11 candies, how many candies does Ava have? How many candies does Noah have? Write two equations to solve the problem.

• Ava has 25 candies, Noah has 16 candies

• Ava has 23 candies, Noah has 14 candies

• Ava has 21 candies, Noah has 12 candies

• Ava has 19 candies, Noah has 10 candies

Answer explanation

Let O = Olivia's candies, N = Noah's candies, A = Ava's candies. We have O = N - 9 and N = A - 5. Given O = 11, we find N = 20 and A = 23. Thus, Ava has 23 candies and Noah has 14 candies.

Lucas has 3 fewer books than Ethan. Ethan has 7 fewer books than Sophia. If Lucas has 9 books, how many books does Sophia have? How many books does Ethan have? Write two equations to solve the problem.

• Sophia has 19 books, Ethan has 12 books

• Sophia has 21 books, Ethan has 14 books

• Sophia has 23 books, Ethan has 16 books

• Sophia has 25 books, Ethan has 18 books

Answer explanation

Let L = Lucas's books, E = Ethan's books, S = Sophia's books. We have L = E - 3 and E = S - 7. Given L = 9, we find E = 12 and S = 23. Thus, Sophia has 23 books, Ethan has 16 books.

Ella has 6 fewer stickers than Liam. Liam has 4 fewer stickers than Chloe. If Ella has 7 stickers, how many stickers does Chloe have? How many stickers does Liam have? Write two equations to solve the problem.

• Chloe has 17 stickers, Liam has 11 stickers

• Chloe has 15 stickers, Liam has 9 stickers

• Chloe has 13 stickers, Liam has 7 stickers

• Chloe has 11 stickers, Liam has 5 stickers

Answer explanation

Let E be Ella's stickers, L Liam's, and C Chloe's. We have E = L - 6 and L = C - 4. Given E = 7, we find L = 13 and C = 17. Thus, Chloe has 17 stickers and Liam has 11 stickers.

Mason has 8 fewer coins than Logan. Logan has 2 fewer coins than Zoe. If Mason has 6 coins, how many coins does Zoe have? How many coins does Logan have? Write two equations to solve the problem.

• Zoe has 16 coins, Logan has 10 coins

• Zoe has 14 coins, Logan has 8 coins

• Zoe has 12 coins, Logan has 6 coins

• Zoe has 10 coins, Logan has 4 coins

Answer explanation

Let M be Mason's coins, L be Logan's, and Z be Zoe's. We have M = L - 8 and L = Z - 2. Given M = 6, we find L = 14 and Z = 16. Thus, Zoe has 14 coins and Logan has 8 coins, matching the correct choice.

Aiden has 5 fewer balloons than Harper. Harper has 3 fewer balloons than Grace. If Aiden has 4 balloons, how many balloons does Grace have? How many balloons does Harper have? Write two equations to solve the problem.

• Grace has 12 balloons, Harper has 7 balloons

• Grace has 10 balloons, Harper has 5 balloons

• Grace has 8 balloons, Harper has 3 balloons

• Grace has 6 balloons, Harper has 1 balloon

Answer explanation

Let A = Aiden's balloons, H = Harper's, G = Grace's. A = H - 5 and H = G - 3. Given A = 4, we find H = 9 and G = 12. Thus, Grace has 12 balloons and Harper has 7 balloons.

Isabella has 10 fewer toys than James. James has 5 fewer toys than Amelia. If Isabella has 15 toys, how many toys does Amelia have? How many toys does James have? Write two equations to solve the problem.

• Amelia has 30 toys, James has 20 toys

• Amelia has 28 toys, James has 18 toys

• Amelia has 26 toys, James has 16 toys

• Amelia has 24 toys, James has 14 toys

Answer explanation

Let I = Isabella's toys, J = James's toys, A = Amelia's toys. We have I = J - 10 and J = A - 5. Given I = 15, we find J = 25 and A = 30. Thus, Amelia has 30 toys, James has 20 toys.

Sophia has 2 fewer cookies than Jackson. Jackson has 6 fewer cookies than Mia. If Sophia has 8 cookies, how many cookies does Mia have? How many cookies does Jackson have? Write two equations to solve the problem.

• Mia has 16 cookies, Jackson has 10 cookies

• Mia has 14 cookies, Jackson has 8 cookies

• Mia has 12 cookies, Jackson has 6 cookies

• Mia has 10 cookies, Jackson has 4 cookies

Answer explanation

Let S = Sophia's cookies, J = Jackson's cookies, M = Mia's cookies. We have S = J - 2 and J = M - 6. Given S = 8, we find J = 10 and M = 16. Thus, Mia has 16 cookies and Jackson has 10 cookies.